# How do you write the expression 4^(4/3) in radical form?

Apr 18, 2017

$\sqrt[3]{{4}^{4}}$

#### Explanation:

${a}^{\frac{\textcolor{red}{n}}{\textcolor{g r e e n}{m}}} = \sqrt[\textcolor{g r e e n}{m}]{{a}^{\textcolor{red}{n}}}$

So ${4}^{\frac{\textcolor{red}{4}}{\textcolor{g r e e n}{3}}} = \sqrt[\textcolor{g r e e n}{3}]{{4}^{\textcolor{red}{4}}}$

Apr 18, 2017

See the entire solution process below:

#### Explanation:

First, we can use this rule of exponents to rewrite the expression:

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

${4}^{\frac{4}{3}} = {4}^{\textcolor{red}{4} \times \textcolor{b l u e}{\frac{1}{3}}} = {\left({4}^{\textcolor{red}{4}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}} = {256}^{\frac{1}{3}}$

We can now use this rule of exponents to write this expression in radical form:

${x}^{\frac{1}{\textcolor{red}{n}}} = \sqrt[\textcolor{red}{n}]{x}$

${256}^{\frac{1}{\textcolor{red}{3}}} = \sqrt[\textcolor{red}{3}]{256}$