# How do you write root3(8^2) as a fractional exponent?

May 25, 2017

See a solution process below:

#### Explanation:

First use this rule to eliminate the radical:

$\sqrt[\textcolor{red}{n}]{x} = {x}^{\frac{1}{\textcolor{red}{n}}}$

$\sqrt[\textcolor{red}{3}]{{8}^{2}} \implies {\left({8}^{2}\right)}^{\frac{1}{\textcolor{red}{3}}}$

Now, use this rule to combine the exponents:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({8}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}} \implies {8}^{\textcolor{red}{2} \times \textcolor{b l u e}{\frac{1}{3}}} \implies {8}^{\frac{2}{3}}$