Question

Simplifique a expressão, de forma que o denominador seja racional: $\sqrt{ \frac{x}{y}$ vezes $\sqrt[3]{ \frac{y}{x} }$ sendo que x, y ∈ R*+

Answer 1

$\ = \sqrt{\frac{x}{y}} \cdot\sqrt[3]{\frac{y}{x}}\\ \\=\sqrt[6]{(\frac{x}{y})^3} \cdot\sqrt[6]{(\frac{y}{x})^2}\\ \\ =\sqrt[6]{(\frac{x}{y})^3 \cdot(\frac{y}{x})^2}\\ \\ =\sqrt[6]{(\frac{x}{y})^3 \cdot(\frac{x}{y})^{-2}}\\ \\ =\sqrt[6]{(\frac{x}{y})^{3-2}} \\ =\sqrt[6]{(\frac{x}{y})^1} \\ =\sqrt[6]{\frac{x}{y}}$