# How do you simplify (27p^6)^(5/3)?

Sep 9, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

${\left({3}^{3} {p}^{6}\right)}^{\frac{5}{3}}$

Now, use this rule of exponents to simplify the expression:

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

${\left({3}^{\textcolor{red}{3}} {p}^{\textcolor{red}{6}}\right)}^{\textcolor{b l u e}{\frac{5}{3}}} \implies {3}^{\textcolor{red}{3} \times \textcolor{b l u e}{\frac{5}{3}}} {9}^{\textcolor{red}{6} \times \textcolor{b l u e}{\frac{5}{3}}} \implies {3}^{\frac{15}{3}} {p}^{\frac{30}{3}} \implies {3}^{5} {p}^{10} \implies$

$243 {p}^{10}$