Answer
$ \frac{216x^{6}}{125y^{6}}$.
Work Step by Step
The given expression is
$=\left ( \frac{5x^{-2}}{6y^{-2}} \right )^{-3}$
Use the law of exponents $(\frac{a}{b})^n=\frac{a^{n}}{ b^n}$
$= \frac{(5x^{-2})^{-3}}{(6y^{-2})^{-3}}$
Use the law of exponents $(ab)^n=a^{n} b^n$
$= \frac{(5)^{-3}(x^{-2})^{-3}}{(6)^{-3}(y^{-2})^{-3}}$
Use the law of exponents $(a^m)^n=a^{m\cdot n}$
$= \frac{5^{-3}x^{-2\cdot-3}}{6^{-3}y^{-2\cdot -3}}$
Simplify.
$= \frac{5^{-3}x^{6}}{6^{-3}y^{6}}$
Use the law of exponents $a^{-n}=\frac{1}{a^{n}}$
$= \frac{6^{3}x^{6}}{5^{3}y^{6}}$
Use $6^3=216$ and $5^3=125$.
$= \frac{216x^{6}}{125y^{6}}$.
