# How do you write root5((7x)^4) as an equivalent expression using a fractional exponent?

Jan 10, 2017

${\left(7 x\right)}^{\frac{4}{5}}$

#### Explanation:

First, we need to convert this radical form to an exponent form using this rule:

$\sqrt[\textcolor{red}{n}]{\textcolor{b l u e}{x}} = {\textcolor{b l u e}{x}}^{\frac{1}{\textcolor{red}{n}}}$

Using this rule:

$\sqrt[\textcolor{red}{5}]{\textcolor{b l u e}{{\left(7 x\right)}^{4}}} \to {\left(\textcolor{b l u e}{{\left(7 x\right)}^{4}}\right)}^{\textcolor{red}{\frac{1}{5}}}$

We can now use this following rule for exponents to further simplify:

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

${\left(\textcolor{b l u e}{{\left(7 x\right)}^{4}}\right)}^{\textcolor{red}{\frac{1}{5}}} \to {\textcolor{b l u e}{\left(7 x\right)}}^{4 \times \textcolor{red}{\frac{1}{5}}} \to {\left(7 x\right)}^{\frac{4}{5}}$