# How do you simplify (xy)^pi?

Sep 10, 2017

See a solution process below:

#### Explanation:

We can rewrite the expression within the parenthesis using this rule of exponents:

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

${\left(x y\right)}^{\pi} \implies {\left({x}^{\textcolor{red}{1}} {y}^{\textcolor{red}{1}}\right)}^{\pi}$

We can now eliminate the outer exponent using this rule of exponents:

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

${\left({x}^{\textcolor{red}{1}} {y}^{\textcolor{red}{1}}\right)}^{\textcolor{b l u e}{\pi}} \implies {x}^{\textcolor{red}{1} \times \textcolor{b l u e}{\pi}} {y}^{\textcolor{red}{1} \times \textcolor{b l u e}{\pi}} \implies {x}^{\pi} {y}^{\pi}$