Question

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

Answer 1

`As\text{ a radical expression =}\sqrt[9]{3}`Step-by-step explanation:
`(3^{(2)/(3)})^{(1)/(6)}`

First we solve the expression in the parenthesis:

`3^{(2)/(3)^{}}=\sqrt[3]{3^2}\text{ = }\sqrt[3]{9}`
`\begin{gathered} \sqrt[3]{9}=9^{(1)/(3)} \\ (3^{(2)/(3)})^{(1)/(6)}\text{ }=(9^{(1)/(3)})^{(1)/(6)} \\ =9^{(1)/(3)*(1)/(6)} \end{gathered}`
`\begin{gathered} =9^{(1)/(18)}=3^{2*(1)/(18)} \\ =3^{(2)/(18)}=3^{(1)/(9)} \\ 9^{(1)/(3)}=\sqrt[9]{3} \end{gathered}`