Answer
$ \frac{16x^{2}}{9y^{2}}$.
Work Step by Step
The given expression is
$=\left ( \frac{3x^{-1}}{4y^{-1}} \right )^{-2}$
Use the law of exponents $(\frac{a}{b})^n=\frac{a^{n}}{ b^n}$
$= \frac{(3x^{-1})^{-2}}{(4y^{-1})^{-2}}$
Use the law of exponents $(ab)^n=a^{n} b^n$
$= \frac{(3)^{-2}(x^{-1})^{-2}}{(4)^{-2}(y^{-1})^{-2}}$
Use the law of exponents $(a^m)^n=a^{m\cdot n}$
$= \frac{3^{-2}x^{-1\cdot-2}}{4^{-2}y^{-1\cdot -2}}$
Simplify.
$= \frac{3^{-2}x^{2}}{4^{-2}y^{2}}$
Use the law of exponents $a^{-n}=\frac{1}{a^{n}}$
$= \frac{4^{2}x^{2}}{3^{2}y^{2}}$
Use $4^=16$ and $3^2=9$.
$= \frac{16x^{2}}{9y^{2}}$.
