Answer
$\dfrac{y^2}{z^7}$
Work Step by Step
Using laws of exponents, the given expression simplifies to
\begin{align*}
&
\left( \dfrac{3z^{-2}}{y} \right)^2\left( \dfrac{9y^{-4}}{z^{-3}} \right)^{-1}
\\\\&=
\left( \dfrac{3^2z^{-2(2)}}{y^2} \right)\left( \dfrac{9^{-1}y^{-4(-1)}}{z^{-3(-1)}} \right)
\\\\&=
\left( \dfrac{9z^{-4}}{y^2} \right)\left( \dfrac{y^{4}}{9^{}z^{3}} \right)
\\\\&=
\dfrac{9z^{-4}y^4}{9y^2z^3}
\\\\&=
(9\div9)z^{-4-3}y^{4-2}
\\\\&=
z^{-7}y^{2}
\\\\&=
\dfrac{y^2}{z^7}
.\end{align*}
