Answer
$\dfrac{y^{6}}{36x^{4}z^{4}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
(-6x^2y^{-3}z^2)^{-2}
.$
$\bf{\text{Solution Details:}}$
Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(-6)^{-2}x^{2(-2)}y^{-3(-2)}z^{2(-2)}
\\\\=
(-6)^{-2}x^{-4}y^{6}z^{-4}
.\end{array}
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{y^{6}}{(-6)^{2}x^{4}z^{4}}
\\\\=
\dfrac{y^{6}}{36x^{4}z^{4}}
.\end{array}
