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