Question

Вычислите
$48^{2/5} *\frac{4}{9}^{1/5}$
$\sqrt[5]{64} /2^{-1/5} *2^{3/5}$

Answer 1

Решение:

$48^{\frac{2}{5} } * (\frac{4}{9})^{\frac{1}{5} } = 48^{\frac{2}{5} } * \frac{4^{\frac{1}{5} } }{9^{\frac{1}{5} }} = \sqrt[5]{48^{2} } * \frac{\sqrt[5]{4} }{\sqrt[5]{9} } = \frac{\sqrt[5]{48^{2}*4 } }{\sqrt[5]{9}} = \frac{\sqrt[5]{2304*4 } }{\sqrt[5]{9}} = \frac{2\sqrt[5]{72*4} }{\sqrt[5]{9}} = \frac{2\sqrt[5]{288} }{\sqrt[5]{9}} = \frac{4\sqrt[5]{9} }{\sqrt[5]{9}} = 4$

$(\frac{\sqrt[5]{64} }{2})^{-\frac{1}{5} } * 2^{\frac{3}{5} } = 2^{-\frac{1}{10} } * 2^{\frac{3}{5} } = 2^{\frac{1}{2} } = \sqrt{2}$