Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{{(x{y}^{-3})}^{2}}{{(\frac{1}{{x}^{2}}y)}^{3}}\]
Simplify \(\frac{1}{{x}^{2}}y\) to \(\frac{y}{{x}^{2}}\).
\[\frac{{(x{y}^{-3})}^{2}}{{(\frac{y}{{x}^{2}})}^{3}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{x}^{2}{({y}^{-3})}^{2}}{{(\frac{y}{{x}^{2}})}^{3}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{2}{y}^{-6}}{{(\frac{y}{{x}^{2}})}^{3}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{{x}^{2}\times \frac{1}{{y}^{6}}}{{(\frac{y}{{x}^{2}})}^{3}}\]
Simplify \({x}^{2}\times \frac{1}{{y}^{6}}\) to \(\frac{{x}^{2}}{{y}^{6}}\).
\[\frac{\frac{{x}^{2}}{{y}^{6}}}{{(\frac{y}{{x}^{2}})}^{3}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{{x}^{2}}{{y}^{6}}}{\frac{{y}^{3}}{{({x}^{2})}^{3}}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{{x}^{2}}{{y}^{6}}}{\frac{{y}^{3}}{{x}^{6}}}\]
Invert and multiply.
\[\frac{{x}^{2}}{{y}^{6}}\times \frac{{x}^{6}}{{y}^{3}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{{x}^{2}{x}^{6}}{{y}^{6}{y}^{3}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{x}^{2+6}}{{y}^{6}{y}^{3}}\]
Simplify \(2+6\) to \(8\).
\[\frac{{x}^{8}}{{y}^{6}{y}^{3}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{x}^{8}}{{y}^{6+3}}\]
Simplify \(6+3\) to \(9\).
\[\frac{{x}^{8}}{{y}^{9}}\]
x^8/y^9
