Question

вычислите.. 11 класс

$\sqrt[4]{2^{5}*3^{5}} *\sqrt[4]{2^{5}*3^{7}}$

Answer 1

$\sqrt[4]{2^{5}*3^{5}}* \sqrt[4]{2^{5}*3^{7}}= \sqrt[4]{2^{4}*2*3^{4}*3*2^{4}*2*3^{4}*3^{3}}=2*3*2*3*3* \sqrt[4]{2^{2}}=108 \sqrt{2}$

Answer 2

$\sqrt[4]{ {2}^{5}* {3}^{5} * {2}^{5} * {3}^{7} } = \sqrt[4]{ {2}^{10}*3 {}^{12} } \sqrt[4]{ {3}^{2}*6 {}^{10} } = \sqrt[4]{ {3}^{2}*6 {}^{10} } = \sqrt[4]{9*6 {}^{10} } = {6}^{2} * \sqrt[4]{9*6 {}^{2} } = 36 \sqrt[4]{9*36} = 36 \sqrt[4]{324} = 108 \sqrt[4]{4} = 108 \sqrt[4]{ {2}^{2} } = 108 \sqrt{2}$