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

User LostBoy
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1 Answer

24 votes
24 votes

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}

User Goldberg
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