# How do you simplify (x^9y)^(1/3)+(xy^(1/9))^3?

Feb 13, 2017

See the entire simplification process below:

#### Explanation:

We will use these rules for exponents to simplify this expression:

$a = {a}^{\textcolor{red}{1}}$ and ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

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

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

${x}^{3} {y}^{\frac{1}{3}} + {x}^{3} {y}^{\frac{1}{3}} = 1 {x}^{3} {y}^{\frac{1}{3}} + 1 {x}^{3} {y}^{\frac{1}{3}} = \left(1 + 1\right) {x}^{3} {y}^{\frac{1}{3}} =$

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