Answer
$\displaystyle \frac{16x^{2}}{9y^{2}}$
Work Step by Step
Apply rule $\displaystyle \quad \left(\frac{a}{b}\right)^{n}=\frac{a^{n}}{b^{n}}$ to obtain:
$\displaystyle \left( \frac{3x^{-1}}{4y^{-1}} \right)^{-2}=\frac{(3x^{-1})^{-2}}{(4y^{-1})^{-2}} \quad $
Apply the rule $\quad (ab)^{n}=a^{n}b^{n}$ to obtain:
$=\displaystyle \frac{(3^{-2})(x^{-1})^{-2}}{(4)^{-2}(y^{-1})^{-2}} \quad $
Apply the rule $\quad (a^{m})^{n}=a^{mn}$ to obtain:
$=\displaystyle \frac{(3^{-2})(x^{2})}{(4^{-2})(y^{2})} \quad $ ...
Apply the rule $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$:
$=\displaystyle \frac{\frac{1}{3^{2}}(x^{2})}{\frac{1}{4^{2}}(y^{2})}$
Simplify using the rule $\dfrac{\frac{1}{a}}{\frac{1}{b}}=\dfrac{b}{a}$ to obtain:
$=\displaystyle \frac{4^{2}(x^{2})}{3^{2}(y^{2})}$
= $\displaystyle \frac{16x^{2}}{9y^{2}}$
