Question

Пожалуйста напишите решение подробно.

Answer 1

$\displaystyle\frac{\sqrt[10]{81}}{\sqrt[5]{-9}}=\frac{\sqrt[10]{9^2}}{\sqrt[5]{-9}}=\frac{\sqrt[5]{9}}{\sqrt[5]{-9}}=\sqrt[5]{\frac{9}{-9}} =\sqrt[5]{-1}=-1\\\\\\ \sqrt[3]{3\sqrt{81}}^2=\sqrt[3]{3\cdot9}^2=\sqrt[3]{3\cdot3^2}^2=\sqrt[3]{3^3}^2=3^2=9\\\\\\ \frac{\sqrt[6]{256}}{\sqrt[3]{-2}}=\frac{\sqrt[6]{2^8}}{\sqrt[3]{-2}}=\frac{\sqrt[3]{2^4}}{\sqrt[3]{-2}}=\sqrt[3]{-\frac{2^4}{2}}=\sqrt[3]{-2^3}=-2$

$\displaystyle9^{\frac{2}{5}}\cdot27^{\frac{2}{5}}=(3^2)^{\frac{2}{5}}\cdot(3^3)^{\frac{2}{5}}=3^{\frac{4}{5}}\cdot3^{\frac{6}{5}}=3^{\frac{10}{5}}=3^2=9$