Question

Пожалуйста напишите решение подробно.

Answer 1

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

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