Use Rule of Zero: \({x}^{0}=1\).
\[\frac{1}{{(4{x}^{-3}{y}^{2})}^{-2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{{(4\times \frac{1}{{x}^{3}}{y}^{2})}^{-2}}\]
Simplify \(4\times \frac{1}{{x}^{3}}{y}^{2}\) to \(\frac{4{y}^{2}}{{x}^{3}}\).
\[\frac{1}{{(\frac{4{y}^{2}}{{x}^{3}})}^{-2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{\frac{1}{{(\frac{4{y}^{2}}{{x}^{3}})}^{2}}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{1}{\frac{1}{\frac{{(4{y}^{2})}^{2}}{{({x}^{3})}^{2}}}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{1}{\frac{1}{\frac{{4}^{2}{({y}^{2})}^{2}}{{({x}^{3})}^{2}}}}\]
Simplify \({4}^{2}\) to \(16\).
\[\frac{1}{\frac{1}{\frac{16{({y}^{2})}^{2}}{{({x}^{3})}^{2}}}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{1}{\frac{1}{\frac{16{y}^{4}}{{({x}^{3})}^{2}}}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{1}{\frac{1}{\frac{16{y}^{4}}{{x}^{6}}}}\]
Invert and multiply.
\[\frac{1}{\frac{{x}^{6}}{16{y}^{4}}}\]
Invert and multiply.
\[\frac{16{y}^{4}}{{x}^{6}}\]
(16*y^4)/x^6
