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

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