# How do you write 3x^(3/8) exponential expression in radical form?

Jun 7, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$3 {x}^{3 \times \frac{1}{8}}$

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

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

$3 {x}^{\textcolor{red}{3} \times \textcolor{b l u e}{\frac{1}{8}}} \implies 3 {\left({x}^{\textcolor{red}{3}}\right)}^{\textcolor{b l u e}{\frac{1}{8}}}$

Now, use this rule of exponents to write the expression as a radical:

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

$3 {\left({x}^{3}\right)}^{\frac{1}{\textcolor{red}{8}}} = 3 \sqrt[\textcolor{red}{8}]{{x}^{3}}$