Answer
$\dfrac{1}{xy(5y+2x)}$
Work Step by Step
The given expression, $
\dfrac{x^{-2}y^{-2}}{5x^{-1}+2y^{-1}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{1}{x^2y^2}}{\dfrac{5}{x}+\dfrac{2}{y}}
\\\\=
\dfrac{\dfrac{1}{x^2y^2}}{\dfrac{5y+2x}{xy}}
\\\\=
\dfrac{1}{x^2y^2}\div\dfrac{5y+2x}{xy}
\\\\=
\dfrac{1}{x^2y^2}\cdot\dfrac{xy}{5y+2x}
\\\\=
\dfrac{1}{\cancel{xy}\cdot xy}\cdot\dfrac{\cancel{xy}}{5y+2x}
\\\\=
\dfrac{1}{xy(5y+2x)}
.\end{array}
