# How do you write the expression 2^(5/3) in radical form?

Apr 26, 2017

See the solution process below:

#### Explanation:

First, we can rewrite this expression using this rule of exponents:

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

${2}^{\frac{5}{3}} = {2}^{\textcolor{red}{5} \times \textcolor{b l u e}{\frac{1}{3}}} = {\left({2}^{\textcolor{red}{5}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}} = {32}^{\frac{1}{3}}$

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

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

${32}^{\frac{1}{\textcolor{red}{3}}} = \sqrt[\textcolor{red}{3}]{32}$