Question

rewrite the rational exponent as a radical expression. (3^2/3)^1/6

Answer 1

$As\text{ a radical expression =}\sqrt[9]{3}$Explanation:$(3^{\frac{2}{3}})^{\frac{1}{6}}$

First we solve the expression in the parenthesis:

$3^{\frac{2}{3}^{}}=\sqrt[3]{3^2}\text{ = }\sqrt[3]{9}$$\begin{gathered} \sqrt[3]{9}=9^{\frac{1}{3}} \\ (3^{\frac{2}{3}})^{\frac{1}{6}}\text{ }=(9^{\frac{1}{3}})^{\frac{1}{6}} \\ =9^{\frac{1}{3}\times\frac{1}{6}} \end{gathered}$$\begin{gathered} =9^{\frac{1}{18}}=3^{2\times\frac{1}{18}} \\ =3^{\frac{2}{18}}=3^{\frac{1}{9}} \\ 9^{\frac{1}{3}}=\sqrt[9]{3} \end{gathered}$