# How do you write the expression (root3(3a))^4 in exponential form?

Apr 25, 2017

See the entire solution process below:

#### Explanation:

First, use this rule of exponents and radicals to put the term within the parenthesis in exponential form:

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

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

Now, use this rule of exponents to combine the exponents inside and outside the parenthesis:

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

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