# How do you divide (x^2/y^3)^4?

Jul 28, 2015

No division is necessary. They are not the same terms.

Split the exponent $\left[{\left(\frac{{x}^{l}}{{y}^{n}}\right)}^{m} = {\left({x}^{l}\right)}^{m} / {\left({y}^{n}\right)}^{m}\right]$:
$= {\left({x}^{2}\right)}^{4} / {\left({y}^{3}\right)}^{4}$

Apply the exponent $\left[{\left({x}^{n}\right)}^{m} = {x}^{n m}\right]$:
$= \frac{{x}^{2 \cdot 4}}{{y}^{3 \cdot 4}}$

Finish:
$= \textcolor{b l u e}{\frac{{x}^{8}}{{y}^{12}}}$

Normally we do not write negative exponents in our answers by convention, so that is our final answer.