# What is  3^(3/2) in radical form?

Mar 7, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

${3}^{3 \times \frac{1}{2}}$

Next, use this rule of exponents to rewrite the expression again:

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

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

Now, use this rule for exponents and radicals to write the expression in radical form:

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

Let $a = {x}^{3}$

${\left({x}^{3}\right)}^{\frac{1}{\textcolor{red}{2}}} \implies \sqrt[\textcolor{red}{2}]{{x}^{3}} \implies \sqrt{{x}^{3}}$