Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{{({3}^{2})}^{-4}}{{(-2\times \frac{1}{y}{z}^{2})}^{-2}}\]
Simplify \(2\times \frac{1}{y}{z}^{2}\) to \(\frac{2{z}^{2}}{y}\).
\[\frac{{({3}^{2})}^{-4}}{{(-\frac{2{z}^{2}}{y})}^{-2}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{3}^{-8}}{{(-\frac{2{z}^{2}}{y})}^{-2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{{3}^{8}}}{{(-\frac{2{z}^{2}}{y})}^{-2}}\]
Simplify \({3}^{8}\) to \(6561\).
\[\frac{\frac{1}{6561}}{{(-\frac{2{z}^{2}}{y})}^{-2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{6561}}{\frac{1}{{(-\frac{2{z}^{2}}{y})}^{2}}}\]
Since the power of 2 is even, the result will be positive.
\[\frac{\frac{1}{6561}}{\frac{1}{{(\frac{2{z}^{2}}{y})}^{2}}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{6561}}{\frac{1}{\frac{{(2{z}^{2})}^{2}}{{y}^{2}}}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{\frac{1}{6561}}{\frac{1}{\frac{{2}^{2}{({z}^{2})}^{2}}{{y}^{2}}}}\]
Simplify \({2}^{2}\) to \(4\).
\[\frac{\frac{1}{6561}}{\frac{1}{\frac{4{({z}^{2})}^{2}}{{y}^{2}}}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{1}{6561}}{\frac{1}{\frac{4{z}^{4}}{{y}^{2}}}}\]
Invert and multiply.
\[\frac{\frac{1}{6561}}{\frac{{y}^{2}}{4{z}^{4}}}\]
Invert and multiply.
\[\frac{1}{6561}\times \frac{4{z}^{4}}{{y}^{2}}\]
Simplify.
\[\frac{4{z}^{4}}{6561{y}^{2}}\]
(4*z^4)/(6561*y^2)
