# How do you simplify ((2/3)^(2/3))^6?

Mar 6, 2017

See the entire simplification process below:

#### Explanation:

First, use this rule of exponents to simplify the exponents on the out parenthesis: ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({\left(\frac{2}{3}\right)}^{\textcolor{red}{\frac{2}{3}}}\right)}^{\textcolor{b l u e}{6}} = {\left(\frac{2}{3}\right)}^{\textcolor{red}{\frac{2}{3}} \times \textcolor{b l u e}{6}} = {\left(\frac{2}{3}\right)}^{4}$

We can now complete the simplification as follows:

${\left(\frac{2}{3}\right)}^{4} = {2}^{4} / {3}^{4} = \frac{16}{81}$