Answer
$\dfrac{7x^{9}y^{5}}{2}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{7x^{-1}y}{14(x^5y^2)^{-2}}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{7x^{-1}y}{14(x^{5(-2)}y^{2(-2)})}
\\\\=
\dfrac{7x^{-1}y}{14x^{-10}y^{-4}}
\\\\=
\dfrac{7x^{-1-(-10)}y^{1-(-4)}}{2}
\\\\=
\dfrac{7x^{-1+10}y^{1+4}}{2}
\\\\=
\dfrac{7x^{9}y^{5}}{2}
.\end{array}
