# How do you simplify (5x ^ { 6} y ^ { 4} ) ^ { 2}?

Jun 20, 2018

See a solution process below:

#### Explanation:

First, use this rule for exponents to rewrite the $5$ term.

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

${\left(5 {x}^{6} {y}^{4}\right)}^{2} \implies {\left({5}^{\textcolor{red}{1}} {x}^{6} {y}^{4}\right)}^{2}$

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

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

${\left({5}^{\textcolor{red}{1}} {x}^{\textcolor{red}{6}} {y}^{\textcolor{red}{4}}\right)}^{\textcolor{b l u e}{2}} \implies {5}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} {x}^{\textcolor{red}{6} \times \textcolor{b l u e}{2}} {y}^{\textcolor{red}{4} \times \textcolor{b l u e}{2}} \implies {5}^{2} {x}^{12} {y}^{8} \implies 25 {x}^{12} {y}^{8}$