# How do you write x^(2/3) in radical form?

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Aug 9, 2017

See a solution process below:

#### Explanation:

First, we can rewrite the term as:

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

Next, we can use this rule of exponents to rewrite the term again:

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

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

Now, we can use this rule to write the term as an radical:

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

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

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