# How do you simplify (a^(4/5) * c^(-1/3))^5?

Feb 9, 2017

See the entire simplification process below:

#### Explanation:

First, apply this rule for exponents:

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

${\left({a}^{\textcolor{red}{\frac{4}{5}}} \cdot {c}^{\textcolor{red}{- \frac{1}{3}}}\right)}^{\textcolor{b l u e}{5}} \to {a}^{\textcolor{red}{\frac{4}{5}} \times \textcolor{b l u e}{5}} \cdot {c}^{\textcolor{red}{- \frac{1}{3}} \times \textcolor{b l u e}{5}} \to {a}^{4} \cdot {c}^{- \frac{5}{3}}$

If we want to have this simplified having no negative exponents we can use this rule for exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${a}^{4} \cdot {c}^{\textcolor{red}{- \frac{5}{3}}} \to {a}^{4} / {c}^{- \textcolor{red}{- \frac{5}{3}}} \to {a}^{4} / {c}^{\textcolor{red}{\frac{5}{3}}}$