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pretraining/mathematica/counting_and_statistics/geometric_mean/11762.txt

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+Problem:
+Compute the geometric mean of ${2401, 25, 64, 4096, 5}$.
+Answer:
+$8\ 7^{4/5} 10^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/13703.txt

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+Problem:
+Compute the geometric mean of ${625, 256, 6, -1, -512}$.
+Answer:
+$8\ 2^{3/5} \sqrt[5]{3} 5^{4/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/13834.txt

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+Problem:
+Compute the geometric mean of ${-1000, 100, 4096, 9, 243, 8}$.
+Answer:
+$24 \sqrt[6]{-3} \sqrt[3]{2} 5^{5/6}$

pretraining/mathematica/counting_and_statistics/geometric_mean/14448.txt

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+Problem:
+Compute the geometric mean of ${1, 1, -512, -7776, 1}$.
+Answer:
+$12\ 2^{4/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/14876.txt

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+Problem:
+Compute the geometric mean of ${25, 3}$.
+Answer:
+$5 \sqrt{3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/15313.txt

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+Problem:
+Compute the geometric mean of ${64, 7, 36}$.
+Answer:
+$4\ 6^{2/3} \sqrt[3]{7}$

pretraining/mathematica/counting_and_statistics/geometric_mean/15655.txt

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+Problem:
+Compute the geometric mean of ${9, 16807, 343, 243, 36}$.
+Answer:
+$21\ 2^{2/5} 3^{4/5} 7^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/21408.txt

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+Problem:
+Compute the geometric mean of ${-10, -125, 1, 9, 10000}$.
+Answer:
+$10\ 3^{2/5} 5^{3/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/24752.txt

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+Problem:
+Compute the geometric mean of ${64, 15625, 625, -7776, 256, 81}$.
+Answer:
+$120 \sqrt[6]{-2} \sqrt{3} 5^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/26452.txt

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+Problem:
+Compute the geometric mean of ${81, 4, 1, 625}$.
+Answer:
+$15 \sqrt{2}$

pretraining/mathematica/counting_and_statistics/geometric_mean/29009.txt

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+Problem:
+Compute the geometric mean of ${-27, 36, -3}$.
+Answer:
+$9\ 2^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/29565.txt

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+Problem:
+Compute the geometric mean of ${-64, 1000, 9}$.
+Answer:
+$40 \sqrt[3]{-1} 3^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/30398.txt

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+Problem:
+Compute the geometric mean of ${-5, 49, 16}$.
+Answer:
+$2 \sqrt[3]{-10} 7^{2/3}$

pretraining/mathematica/counting_and_statistics/geometric_mean/31737.txt

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+Problem:
+Compute the geometric mean of ${256, 36, 49, -59049, 64}$.
+Answer:
+$72 \sqrt[5]{-2} 21^{2/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/31745.txt

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+Problem:
+Compute the geometric mean of ${8, -2, -7}$.
+Answer:
+$2 \sqrt[3]{14}$

pretraining/mathematica/counting_and_statistics/geometric_mean/33464.txt

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+Problem:
+Compute the geometric mean of ${512, 16, 7, 81, -7776}$.
+Answer:
+$24 \sqrt[5]{-7} 2^{3/5} 3^{4/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/36331.txt

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+Problem:
+Compute the geometric mean of ${36, 16807, 216, 1, -7776, 117649}$.
+Answer:
+$42 \sqrt[6]{-1} 6^{2/3} 7^{5/6}$

pretraining/mathematica/counting_and_statistics/geometric_mean/37381.txt

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+Problem:
+Compute the geometric mean of ${1, 16, 5}$.
+Answer:
+$2 \sqrt[3]{10}$

pretraining/mathematica/counting_and_statistics/geometric_mean/38512.txt

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+Problem:
+Compute the geometric mean of ${25, -59049, 16, 25, 25}$.
+Answer:
+$45 \sqrt[5]{-5} 2^{4/5}$

pretraining/mathematica/counting_and_statistics/geometric_mean/39370.txt

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+Problem:
+Compute the geometric mean of ${1, 1296, 512, -27}$.
+Answer:
+$(12+12 i) 6^{3/4}$

pretraining/mathematica/counting_and_statistics/geometric_mean/42387.txt

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+Problem:
+Compute the geometric mean of ${81, 10, 3}$.
+Answer:
+$3\ 3^{2/3} \sqrt[3]{10}$

pretraining/mathematica/counting_and_statistics/geometric_mean/44105.txt

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+Problem:
+Compute the geometric mean of ${49, -16807, 64, 36, 81, 3}$.
+Answer:
+$42 \sqrt[6]{-21} \sqrt[3]{2}$

pretraining/mathematica/counting_and_statistics/geometric_mean/44567.txt

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+Problem:
+Compute the geometric mean of ${-512, 625, -10, 49}$.
+Answer:
+$20 \sqrt[4]{5} \sqrt{14}$

pretraining/mathematica/counting_and_statistics/geometric_mean/45249.txt

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+Problem:
+Compute the geometric mean of ${3, 3, 64, 9}$.
+Answer:
+$6 \sqrt{2}$

pretraining/mathematica/counting_and_statistics/geometric_mean/49885.txt

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

pretraining/mathematica/counting_and_statistics/geometric_mean/6079.txt

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+Problem:
+Compute the geometric mean of ${16, -6, -1, 343, 8}$.
+Answer:
+$2 \sqrt[5]{3} 14^{3/5}$

pretraining/mathematica/number_theory/lcm/13310.txt

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+Problem:
+Find the least common multiple of $\left\{1,-\frac{14}{9},4\right\}$.
+Answer:
+$28$

pretraining/mathematica/number_theory/lcm/14085.txt

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+Problem:
+Find the least common multiple of $\left\{-2,-\frac{11}{3}\right\}$.
+Answer:
+$22$

pretraining/mathematica/number_theory/lcm/1419.txt

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+Problem:
+Find the least common multiple of $\left\{0,4,2,\frac{4}{3}\right\}$.
+Answer:
+$0$

pretraining/mathematica/number_theory/lcm/15377.txt

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+Problem:
+Find the least common multiple of $\left\{\frac{8}{3},-4\right\}$.
+Answer:
+$8$

pretraining/mathematica/number_theory/lcm/15766.txt

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+Problem:
+Find the least common multiple of $\left\{\frac{10}{3},1,5,3\right\}$.
+Answer:
+$30$

pretraining/mathematica/number_theory/lcm/15944.txt

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+Problem:
+Find the least common multiple of $\left\{\frac{5}{2},\frac{13}{9},\frac{22}{9}\right\}$.
+Answer:
+$1430$

pretraining/mathematica/number_theory/lcm/16502.txt

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+Problem:
+Find the least common multiple of $\{0,-1\}$.
+Answer:
+$0$

pretraining/mathematica/number_theory/lcm/1695.txt

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+Problem:
+Find the least common multiple of $\left\{\frac{10}{3},-\frac{11}{3},1\right\}$.
+Answer:
+$110$

pretraining/mathematica/number_theory/lcm/17107.txt

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+Problem:
+Find the least common multiple of $\left\{\frac{12}{7},1,0,-5\right\}$.
+Answer:
+$0$

pretraining/mathematica/number_theory/lcm/17109.txt

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+Problem:
+Find the least common multiple of $\left\{\frac{14}{5},-1,2\right\}$.
+Answer:
+$14$

pretraining/mathematica/number_theory/lcm/1743.txt

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+Problem:
+Find the least common multiple of $\{-4,4,-1,4\}$.
+Answer:
+$4$

pretraining/mathematica/number_theory/lcm/17546.txt

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+Problem:
+Find the least common multiple of $\{-3,5,1,4\}$.
+Answer:
+$60$

pretraining/mathematica/number_theory/lcm/20173.txt

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+Problem:
+Find the least common multiple of $\left\{-\frac{38}{9},\frac{6}{5},0\right\}$.
+Answer:
+$0$

pretraining/mathematica/number_theory/lcm/20877.txt

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+Problem:
+Find the least common multiple of $\left\{2,-\frac{4}{7}\right\}$.
+Answer:
+$4$

pretraining/mathematica/number_theory/lcm/21339.txt

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+Problem:
+Find the least common multiple of $\left\{5,\frac{31}{9},3\right\}$.
+Answer:
+$465$

pretraining/mathematica/number_theory/lcm/22241.txt

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+Problem:
+Find the least common multiple of $\left\{-\frac{29}{9},3,-1,-1\right\}$.
+Answer:
+$87$

pretraining/mathematica/number_theory/lcm/22415.txt

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+Problem:
+Find the least common multiple of $\{5,-2\}$.
+Answer:
+$10$

pretraining/mathematica/number_theory/lcm/22659.txt

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+Problem:
+Find the least common multiple of $\left\{-4,-\frac{5}{2}\right\}$.
+Answer:
+$20$

pretraining/mathematica/number_theory/lcm/23706.txt

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+Problem:
+Find the least common multiple of $\left\{1,-\frac{35}{9}\right\}$.
+Answer:
+$35$

pretraining/mathematica/number_theory/lcm/24349.txt

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+Problem:
+Find the least common multiple of $\{-3,0,4\}$.
+Answer:
+$0$

pretraining/mathematica/number_theory/lcm/25144.txt

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+Problem:
+Find the least common multiple of $\left\{-3,-2,-\frac{31}{7}\right\}$.
+Answer:
+$186$

pretraining/mathematica/number_theory/lcm/25206.txt

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+Problem:
+Find the least common multiple of $\{-5,-5\}$.
+Answer:
+$5$

pretraining/mathematica/number_theory/lcm/26121.txt

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+Problem:
+Find the least common multiple of $\left\{-\frac{5}{2},-3,3\right\}$.
+Answer:
+$15$

pretraining/mathematica/number_theory/lcm/26778.txt

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+Problem:
+Find the least common multiple of $\left\{-3,-1,-\frac{9}{2},0\right\}$.
+Answer:
+$0$