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

Aug 29, 2017

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

#### Explanation:

$\text{Fractional exponents are expressed in radical form using}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{a}^{\frac{m}{n}} = \sqrt[n]{{a}^{m}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow {4}^{\frac{4}{3}} = \sqrt[3]{{4}^{4}}$

Aug 29, 2017

See a solution process below

#### Explanation:

First, rewrite the expression as:

${4}^{4 \cdot \frac{1}{3}}$

Use this rule to rewrite the expression again:

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

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

When can then use this rule to rewrite the expression in radical form:

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

$\left({4}^{4}\right) {x}^{\frac{1}{\textcolor{red}{3}}} = \sqrt[\textcolor{red}{3}]{{4}^{4}}$

If necessary, we can simplify the term within the radical as:

$\sqrt[3]{{4}^{4}} = \sqrt[3]{256}$

Also, if necessary, we can simply the term within the radical using this rule:

$\sqrt[n]{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt[n]{\textcolor{red}{a}} \cdot \sqrt[n]{\textcolor{b l u e}{b}}$

$\sqrt[3]{{4}^{4}} = \sqrt[3]{\textcolor{red}{{4}^{3}} \cdot \textcolor{b l u e}{4}} = \sqrt[3]{\textcolor{red}{{4}^{3}}} \cdot \sqrt[3]{\textcolor{b l u e}{4}} = 4 \sqrt[3]{4}$