# How do you write 4^(2/3) * a^(1/3)  in radical form?

Jul 21, 2017

See a solution process below:

#### Explanation:

First, rewrite the $4$ term as:

${4}^{2 \times \frac{1}{3}} \cdot {a}^{\frac{1}{3}}$

Next, use this rule of exponents to rewrite the $4$ term again:

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

${\left({4}^{2}\right)}^{\frac{1}{3}} \cdot {a}^{\frac{1}{3}} \implies {16}^{\frac{1}{3}} \cdot {a}^{\frac{1}{3}} \implies {\left(16 a\right)}^{\frac{1}{3}}$

Next, use this rule to put the expression into radical form:

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

${\left(16 a\right)}^{\frac{1}{\textcolor{red}{3}}} \implies \sqrt[\textcolor{red}{3}]{16 a}$

If necessary we can rewrite this as:

$\sqrt[3]{16 a} \implies \sqrt[3]{8 \cdot 2 a} \implies \sqrt[3]{8} \sqrt[3]{2 a} \implies 2 \sqrt[3]{2 a}$