Answer
$\displaystyle \frac{y^{4}}{(xy-1)^{2}}$
Work Step by Step
$(x\cdot y^{-1}-y^{-2})^{-2}$=.........$\displaystyle \frac{1}{a^{n}}=a^{-n}$
$=[\displaystyle \frac{x}{y}-\frac{1}{y^{2}}]^{-2}$=........common denominator =$y^{2}$
$=[\displaystyle \frac{xy}{y^{2}}-\frac{1}{y^{2}}]^{-2}$
$=[\displaystyle \frac{xy-1}{y^{2}}]^{-2}$=.........$\displaystyle \frac{1}{a^{n}}=a^{-n}$
$=[\displaystyle \frac{y^{2}}{xy-1}]^{2}$=.........$(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$
$=\displaystyle \frac{(y^{2})^{2}}{(xy-1)^{2}}$=.........$(a^{m})^{n}=a^{mn}$
$=\displaystyle \frac{y^{4}}{(xy-1)^{2}}$
