# How do you simplify (q^(1/5))^5times(q^(2/3))^3?

Jan 3, 2017

Use various rules for exponents to simplify this expression. See explanation below.

#### Explanation:

The first rule for exponents will will utilize is:

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

This simplifies our expression to:

${q}^{\textcolor{red}{\frac{1}{5}} \times \textcolor{b l u e}{5}} \times {q}^{\textcolor{red}{\frac{2}{3}} \times \textcolor{b l u e}{3}} =$

q^(color(red)(1)) xx q^(color(red)(2)

The next rule of exponents we can use is:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

Using this rule allows us to simplify our expression to:

${q}^{\textcolor{red}{1} + \textcolor{red}{2}} =$

${q}^{3}$