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you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
why is learning exponents so important ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how do you do scientific notation ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power . ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . ''
but i dont get it it does not explain how 3 to the power of 2 witch it does int explain why 3 times 3 is in there ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and when you add those 2 's together , you get 6 . what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . '
is there any sign that shows repeated division ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
if a value have exponent 0 then ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
what if the exponent is over 1000 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how is exponents like basically than addition , subtraction , multiplication , and division ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
can irrational numbers be exponets ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power is equal to 8 . ( 2^3 = 8 . ) let 's try a few more examples here .
what is 5^8 times 4^3 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
what happens when an exponent is negative ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power . ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . ''
how would you evaluate a number raised to a fraction exponent like 4^3/2 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
is there a variable exponent ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . '' but remember , i just said this is repeated multiplication .
would your answers for negative exponents be a positive ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
what if the exponent of a number was negative ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
is there any reason why it is called `` to the power '' ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so this would be equal to , not 2 + 2 + 2 , but 2 × ... ( and i ’ ll use a little dot to signify multiplication . ) ... 2 × 2 × 2 . well , what 's 2 × 2 × 2 ?
what is 2 to the 0 power equal to ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how do you do a fractoin to a negative exponants ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
: ( so how should i answer really hard exponent questions ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
a quick fun question : what 's 9 to the 6th power ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
what are exponents used for ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
wait ... if 100 is 10 to the power 10 , then what do you do to get 200 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's . and we are multiplying them .
why does 5^0 equal 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
so what exactly is an exponent ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
what 's the difference between exponents and scientific notation ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so let 's multiply 3 – ( let me do that in yellow . ) let 's multiply 3 × 3 . so this is going to be equal to 9 .
what is the difference between multiplication that add and exponents that multiply ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and when you add those 2 's together , you get 6 . what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . '
just like exponents are repeated multiplication , is there a mathematical function for repeated division ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
if multiplication is repeated addition and exponents are repeated multiplication , is division repeated subtraction and roots are repeated division ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
what if the exponent is 0 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 .
4 to the power of 0 is 0 , right ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
what difference does the parenthesis make ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
a sign for an exponent can be ^ or e , right ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
when you are asked to `` evaluate '' an exponent what are they asking ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
is 0/0 zero , one , or undefined ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's .
5 to the power of 8 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
if an exponent can be negative , then which number is negative ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how big can the powers go up to ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's . and we are multiplying them .
is 9^0 , 0 or 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
what is anything to the power of 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how do i show the exponents of infinity ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
can you do an exponent to a power that has another exponent ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
what is the answer to an equation when the exponent is 0 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
how come x to the zeroth power = one ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
can an exponent be in a fraction ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( 2 × 2 × 2 = 8 . ) so 2 to the 3rd power is equal to 8 . ( 2^3 = 8 . )
why does a power to 0 equal 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
well , what 's 2 × 2 × 2 ? well that is equal to 8 . ( 2 × 2 × 2 = 8 . )
if 0 x whatever = 0 , how come 0 lots of whatever-number do n't equal 0 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power . ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . ''
why is 3^2 not the same as 2^3 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power . ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . ''
how does `` two to the third '' mean 2^3 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's . and we are multiplying them . we are not adding them .
what is the use of multiplying with a number 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's .
so can i go 5 to the 100th power , or what ever i want that power to be ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
i understand what exponents are and how 975398^0 being 1 and 0 to a positive number gets you to 0 and how 0^0 is undefined ... but why is there repeated addition , which is multiplication , and repeated multiplication , which is the one that i learned today , while there is no repeated subtraction nor division ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
how do you type up an exponent other than ^ ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's .
what would 5 to the zeroeth power be ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so this would be equal to , not 2 + 2 + 2 , but 2 × ... ( and i ’ ll use a little dot to signify multiplication . ) ... 2 × 2 × 2 . well , what 's 2 × 2 × 2 ?
why is 2^2 sometimes called 2 squared ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
if you have 2 to the power of 6 to the power of 5 to the power of 4 to the power of 3 squared to the power of 1 to the power of zero , do you start at one to the power of zero , and 2 to the power of the result , then 3 to the power of that result , and so on ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
is x to the power of 1 basically using the identity property of multiplication ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so if i have 2 to the 3rd power , ( 2^3 ) , this literally means multiplying 3 2 's together . so this would be equal to , not 2 + 2 + 2 , but 2 × ... ( and i ’ ll use a little dot to signify multiplication . ) ... 2 × 2 × 2 .
when can we use exponents in a life situation ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
is 10 to the 100th power the same as 100 to the 10th power ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
what are exponents good for ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . ''
what if the question is with one number with a power and the number it 's being multiplied by has no exponent ( power ) like for example : 2^7 x 3 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
i know 2nd power would be squared , and 3rd power would be cubed , but what would the 4th power be ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
what do you do if the exponent is 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
could there ever be an exponent like 0 to the zeroeth power ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
is there a simple trick to figure out the exponent , base , or value if two of three are known ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
is there a simple trick to figure out the exponent , base , or value if two of three are known ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
what happens when a base has a power that is negative ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
what happens if a base is negative ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power . ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . ''
3^3 is 27 3^2 is 9 3^1 is 3 so everytime you /3 therefore should n't it be 3^0 is 1 not ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so this would be equal to , not 2 + 2 + 2 , but 2 × ... ( and i ’ ll use a little dot to signify multiplication . ) ... 2 × 2 × 2 . well , what 's 2 × 2 × 2 ?
so in exponents 2 to the power of 4 is 2*2*2*2=16 right ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
how would you type an exponent into a keyboard ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's . and we are multiplying them .
so would 1^1 be 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
whay does the negative exponent mean ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power is equal to 8 . ( 2^3 = 8 . ) let 's try a few more examples here .
how do you divide with negative fractions i.e 4.8 / -0.8 = ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how will i know which exponential expression is greater when both the exponent and the base are different without expanding the exponentiation to multiplication ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
what is pi to the power of pi ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
what is something to the power to the power of infinity ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what is , say , 5 to the – let 's say – 5 to the 4th power ( 5^4 ) ? and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together .
find the smallest +ve mathematical number which is spelled in an alphabetical order ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so let 's multiply 3 – ( let me do that in yellow . ) let 's multiply 3 × 3 . so this is going to be equal to 9 .
what would -3 raised to the fourth power be ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
is the base negative three ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how does the negative sign work with the order of operations ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so 2 to the 3rd power is equal to 8 . ( 2^3 = 8 . ) let 's try a few more examples here .
is it possible to do -5^6^7^8^8^8^9^4^3^0.000000000000000000000000000000000000001^434341253451234652134251341435243512432534521345 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
if a number is to the pi power , for example , 2 to the pi power , what would the number equal ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and when you add those 2 's together , you get 6 . what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . '
is there a such thing as repeated division ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
125 × 5 is 625 . ( 125 × 5 = 625 . )
how is 125 times 5 equal to 625 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . )
p=1 how do i find 5p to the 8th power ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
if a value have exponent 0 then ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
what is this symbol called ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
why is exponents so inportant ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so let 's multiply 3 – ( let me do that in yellow . ) let 's multiply 3 × 3 . so this is going to be equal to 9 .
if your working in index form can a negative base value eg -3 be simplified with a positive base value of 3 eg ( -3 ) ^4 x 3^14 can it be represented as 3^56 or can it not be simplified ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
does exponents help with simplifying equations ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
what kind of symbol is ^ ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
if the exponent is 0 why is the answer 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
what is the answer if the base and exponent both are infinity ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
why do we have to make the exponent of 0 1 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and when you add those 2 's together , you get 6 . what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . '
can there be repeated division ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 .
so can we call a number raised to the 4 power as , `` timed '' ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's .
so , 5 to the 4th power.is there a faster way to do it other than 5x5x5x5 ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
so this would be equal to , not 2 + 2 + 2 , but 2 × ... ( and i ’ ll use a little dot to signify multiplication . ) ... 2 × 2 × 2 . well , what 's 2 × 2 × 2 ?
if there are 2 exponents , do we use an exponent , on the origanal exponent ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
how many exponents are possible in one answer ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together .
is there such a relationship between addition and exponents ?
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro...
what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy .
i know the exponent can be any number up to infinity , but can the exponent be infinity ?