# How do you simplify (6py^2)^(1/4)?

Jul 31, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression using this rule of exponents:

$a = {a}^{\textcolor{red}{1}}$

${\left(6 p {y}^{2}\right)}^{\frac{1}{4}} \implies {\left({6}^{\textcolor{red}{1}} {p}^{\textcolor{red}{1}} {y}^{2}\right)}^{\frac{1}{4}}$

Now, use this rule of exponents to eliminate the outer exponent:

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

${\left({6}^{\textcolor{red}{1}} {p}^{\textcolor{red}{1}} {y}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{\frac{1}{4}}} \implies$

${6}^{\textcolor{red}{1} \times \textcolor{b l u e}{\frac{1}{4}}} {p}^{\textcolor{red}{1} \times \textcolor{b l u e}{\frac{1}{4}}} {y}^{\textcolor{red}{2} \times \textcolor{b l u e}{\frac{1}{4}}} \implies$

${6}^{\frac{1}{4}} {p}^{\frac{1}{4}} {y}^{\frac{1}{2}}$

Or

${\left(6 p\right)}^{\frac{1}{4}} {y}^{\frac{1}{2}}$

Or

$\sqrt[4]{6 p} \sqrt{y}$