# Simplify 9^(2/3)#?

Apr 10, 2017

See the entire solution process below:

#### Explanation:

We can use this rule of exponents to rewrite this expression:

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

${9}^{\frac{2}{3}} = {9}^{\textcolor{red}{2} \times \textcolor{b l u e}{\frac{1}{3}}} = {\left({9}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}}$

${9}^{2} = 81$ so we can rewrite this as:

${\left({9}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}} = {81}^{\frac{1}{3}}$

Next, we can use the rule of radicals and exponents to continue the simplification:

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

${81}^{\frac{1}{\textcolor{red}{3}}} = \sqrt[\textcolor{red}{3}]{81}$

Now, we can rewrite the term within the radical and complete the simplification as:

$\sqrt[3]{81} = \sqrt[3]{27 \cdot 3} = \sqrt[3]{27} \sqrt[3]{3} = 3 \sqrt[3]{3}$