# How do you simplify root3(x^4)?

Feb 4, 2017

See the entire simplification process below:

#### Explanation:

The first simplification step will use this rule for exponents in radical form: $\sqrt[\textcolor{red}{n}]{x} = {x}^{\frac{1}{\textcolor{red}{n}}}$

So we can rewrite this expression as:

$\sqrt[\textcolor{red}{3}]{{x}^{4}} = {\left({x}^{4}\right)}^{\frac{1}{\textcolor{red}{3}}}$

We can now use this rule for exponents to complete the simplification: ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({x}^{\textcolor{red}{4}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}} = {x}^{\textcolor{red}{4} \times \textcolor{b l u e}{\frac{1}{3}}} = {x}^{\frac{4}{3}}$