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pretraining/mathematica/counting_and_statistics/geometric_mean/11064.txt

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+Problem:
+Compute the geometric mean of ${-343, -1, -3, 1024, 216}$.
+Answer:
+$4 \sqrt[5]{-1} 3^{4/5} 14^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/12624.txt

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+Problem:
+Compute the geometric mean of ${1, 10, 59049, -32, 1296}$.
+Answer:
+$36 \sqrt[5]{-5} 3^{4/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/15367.txt

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+Problem:
+Compute the geometric mean of ${3, -512, 16, 49}$.
+Answer:
+$8 \sqrt[4]{-6} \sqrt{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/15540.txt

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+Problem:
+Compute the geometric mean of ${6561, 6561, 16, 16}$.
+Answer:
+$324$

pretraining/mathematica/counting_and_statistics/geometric_mean/16000.txt

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+Problem:
+Compute the geometric mean of ${25, 1, -512}$.
+Answer:
+$8 \sqrt[3]{-1} 5^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/16798.txt

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+Problem:
+Compute the geometric mean of ${512, -8, 125, -6, 5}$.
+Answer:
+$4\ 2^{3/5} \sqrt[5]{3} 5^{4/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/17094.txt

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+Problem:
+Compute the geometric mean of ${1024, 1, 49, -32768, -1000}$.
+Answer:
+$32\ 7^{2/5} 10^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/17293.txt

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+Problem:
+Compute the geometric mean of ${9, 7}$.
+Answer:
+$3 \sqrt{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/17712.txt

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+Problem:
+Compute the geometric mean of ${36, 2, 9}$.
+Answer:
+$6 \sqrt[3]{3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/18511.txt

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+Problem:
+Compute the geometric mean of ${2401, 2401, 243, 1000000, -243, -343}$.
+Answer:
+$210\ 3^{2/3} 7^{5/6}$

pretraining/mathematica/counting_and_statistics/geometric_mean/19620.txt

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+Problem:
+Compute the geometric mean of ${-7776, 59049, -16807, 100000, 9}$.
+Answer:
+$3780\ 3^{2/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/20208.txt

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+Problem:
+Compute the geometric mean of ${-125, 2401, 16, 6}$.
+Answer:
+$14 \sqrt[4]{-6} 5^{3/4}$

pretraining/mathematica/counting_and_statistics/geometric_mean/20717.txt

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+Problem:
+Compute the geometric mean of ${512, 2401, 9, 81}$.
+Answer:
+$84 \sqrt[4]{2} \sqrt{3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/2099.txt

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+Problem:
+Compute the geometric mean of ${5, 125, 25, 9}$.
+Answer:
+$5 \sqrt{15}$

pretraining/mathematica/counting_and_statistics/geometric_mean/21723.txt

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+Problem:
+Compute the geometric mean of ${-3, -7}$.
+Answer:
+$\sqrt{21}$

pretraining/mathematica/counting_and_statistics/geometric_mean/22457.txt

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+Problem:
+Compute the geometric mean of ${16807, 16, 1, 256, -3, -27}$.
+Answer:
+$4\ 3^{2/3} 7^{5/6}$

pretraining/mathematica/counting_and_statistics/geometric_mean/23219.txt

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+Problem:
+Compute the geometric mean of ${10, 9, 125}$.
+Answer:
+$5\ 3^{2/3} \sqrt[3]{10}$

pretraining/mathematica/counting_and_statistics/geometric_mean/237.txt

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+Problem:
+Compute the geometric mean of ${9, -4, 9, -1}$.
+Answer:
+$3 \sqrt{2}$

pretraining/mathematica/counting_and_statistics/geometric_mean/24183.txt

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+Problem:
+Compute the geometric mean of ${16, 1000, 36, 216}$.
+Answer:
+$24 \sqrt[4]{3} 5^{3/4}$

pretraining/mathematica/counting_and_statistics/geometric_mean/25093.txt

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+Problem:
+Compute the geometric mean of ${4, 216, 16, 59049, 16}$.
+Answer:
+$36\ 6^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/25625.txt

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+Problem:
+Compute the geometric mean of ${-3, -1, -216, 125}$.
+Answer:
+$(3+3 i) \sqrt[4]{2} 5^{3/4}$

pretraining/mathematica/counting_and_statistics/geometric_mean/27075.txt

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+Problem:
+Compute the geometric mean of ${2401, -9, 15625, 512, -64, -1}$.
+Answer:
+$20 \sqrt[6]{-1} \sqrt{2} \sqrt[3]{3} 7^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/27325.txt

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+Problem:
+Compute the geometric mean of ${-1000, 1, 27, -16807, 10}$.
+Answer:
+$7\ 3^{3/5} 10^{4/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/27739.txt

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+Problem:
+Compute the geometric mean of ${1, 7}$.
+Answer:
+$\sqrt{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/27879.txt

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+Problem:
+Compute the geometric mean of ${1296, 343, 1000000, -8, 64, 16}$.
+Answer:
+$40 \sqrt[6]{-1} 2^{5/6} 3^{2/3} \sqrt{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/29307.txt

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+Problem:
+Compute the geometric mean of ${-4, 1, -4, 16}$.
+Answer:
+$4$

pretraining/mathematica/counting_and_statistics/geometric_mean/30021.txt

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+Problem:
+Compute the geometric mean of ${9, 49, -64, 36}$.
+Answer:
+$(6+6 i) \sqrt{14}$

pretraining/mathematica/counting_and_statistics/geometric_mean/30805.txt

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+Problem:
+Compute the geometric mean of ${1, 49, 64, -125}$.
+Answer:
+$(2+2 i) 5^{3/4} \sqrt{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/31616.txt

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+Problem:
+Compute the geometric mean of ${2, 512, 1000}$.
+Answer:
+$80 \sqrt[3]{2}$

pretraining/mathematica/counting_and_statistics/geometric_mean/31693.txt

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+Problem:
+Compute the geometric mean of ${216, 8, 9, -32, 729}$.
+Answer:
+$36 \sqrt[5]{-6}$

pretraining/mathematica/counting_and_statistics/geometric_mean/32280.txt

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+Problem:
+Compute the geometric mean of ${1, 10, 3}$.
+Answer:
+$\sqrt[3]{30}$

pretraining/mathematica/counting_and_statistics/geometric_mean/32524.txt

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+Problem:
+Compute the geometric mean of ${64, 6}$.
+Answer:
+$8 \sqrt{6}$

pretraining/mathematica/counting_and_statistics/geometric_mean/33638.txt

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+Problem:
+Compute the geometric mean of ${25, -1000, -512, 32, 10}$.
+Answer:
+$40\ 2^{3/5} \sqrt[5]{5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/33894.txt

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+Problem:
+Compute the geometric mean of ${125, 36, 16}$.
+Answer:
+$20\ 3^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/35966.txt

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+Problem:
+Compute the geometric mean of ${-343, -729, -1, 25, 243}$.
+Answer:
+$9 \sqrt[5]{-3} 5^{2/5} 7^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/36565.txt

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+Problem:
+Compute the geometric mean of ${-1, 2, 49, 343}$.
+Answer:
+$7 \sqrt[4]{-14}$

pretraining/mathematica/counting_and_statistics/geometric_mean/40710.txt

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+Problem:
+Compute the geometric mean of ${8, 10}$.
+Answer:
+$4 \sqrt{5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/40953.txt

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+Problem:
+Compute the geometric mean of ${10, 9}$.
+Answer:
+$3 \sqrt{10}$

pretraining/mathematica/counting_and_statistics/geometric_mean/41706.txt

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+Problem:
+Compute the geometric mean of ${1, -125, 36}$.
+Answer:
+$5 \sqrt[3]{-1} 6^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/43529.txt

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+Problem:
+Compute the geometric mean of ${-27, 4, -1}$.
+Answer:
+$3\ 2^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/43749.txt

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+Problem:
+Compute the geometric mean of ${-343, -5, -64, 10000, -1}$.
+Answer:
+$20\ 7^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/45221.txt

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+Problem:
+Compute the geometric mean of ${7, 64}$.
+Answer:
+$8 \sqrt{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/4544.txt

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+Problem:
+Compute the geometric mean of ${6, 4096, -8, 81}$.
+Answer:
+$48 \sqrt[4]{-3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/46192.txt

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+Problem:
+Compute the geometric mean of ${81, 25}$.
+Answer:
+$45$

pretraining/mathematica/counting_and_statistics/geometric_mean/47168.txt

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+Problem:
+Compute the geometric mean of ${16, 7, 531441, 4, 64, 1}$.
+Answer:
+$36 \sqrt[6]{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/493.txt

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+Problem:
+Compute the geometric mean of ${-1, 9, -10, -243, 64, 25}$.
+Answer:
+$6 \sqrt[6]{-6} \sqrt{5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/7812.txt

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+Problem:
+Compute the geometric mean of ${5, 81}$.
+Answer:
+$9 \sqrt{5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/9942.txt

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+Problem:
+Compute the geometric mean of ${125, -27, 64}$.
+Answer:
+$60 \sqrt[3]{-1}$

pretraining/mathematica/counting_and_statistics/geometric_mean/9961.txt

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+Problem:
+Compute the geometric mean of ${8, -8, 64, -27, 117649, 1000}$.
+Answer:
+$28 \sqrt{30}$

pretraining/mathematica/number_theory/lcm/1236.txt

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+Problem:
+Find the least common multiple of $\left\{\frac{14}{3},4,-\frac{5}{3}\right\}$.
+Answer:
+$140$