O inverso de [tex] \sqrt{x/y \sqrt[3]{y/x} [/tex], com x>0 e y>0 é igual a ?.... Pergunta de ideia deTourugo

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

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

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