Question

O inverso de $\sqrt{x/y \sqrt[3]{y/x}$, com x>0 e y>0 é igual a ?

Answer 1

$\sqrt{\frac{x}{y} \sqrt[3]{\frac{y}{x}} }= \sqrt{\frac{x}{y}.(\frac{y}{x})^{\frac{1}{3}}}= \sqrt{\frac{x}{y}.(\frac{x}{y})^{-\frac{1}{3}}}= \sqrt{(\frac{x}{y})^{\frac{2}{3}}} =[(\frac{x}{y})^{\frac{2}{3}}]^{\frac{1}{2}}=(\frac{x}{y})^{\frac{1}{3}}= \sqrt[3]{\frac{x}{y}}\\ \\ O \ inverso:\\ \\ \frac{1}{\sqrt[3]{\frac{x}{y}}}$