Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{4}^{3}{({x}^{2})}^{3}{({y}^{3})}^{3}}{{(3{x}^{3}{y}^{3})}^{3}}\]
Simplify \({4}^{3}\) to \(64\).
\[\frac{64{({x}^{2})}^{3}{({y}^{3})}^{3}}{{(3{x}^{3}{y}^{3})}^{3}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{64{x}^{6}{({y}^{3})}^{3}}{{(3{x}^{3}{y}^{3})}^{3}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{64{x}^{6}{y}^{9}}{{(3{x}^{3}{y}^{3})}^{3}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{64{x}^{6}{y}^{9}}{{3}^{3}{({x}^{3})}^{3}{({y}^{3})}^{3}}\]
Simplify \({3}^{3}\) to \(27\).
\[\frac{64{x}^{6}{y}^{9}}{27{({x}^{3})}^{3}{({y}^{3})}^{3}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{64{x}^{6}{y}^{9}}{27{x}^{9}{({y}^{3})}^{3}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{64{x}^{6}{y}^{9}}{27{x}^{9}{y}^{9}}\]
Cancel \({y}^{9}\).
\[\frac{64{x}^{6}}{27{x}^{9}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[\frac{64{x}^{6-9}}{27}\]
Simplify \(6-9\) to \(-3\).
\[\frac{64{x}^{-3}}{27}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{64\times \frac{1}{{x}^{3}}}{27}\]
Simplify \(64\times \frac{1}{{x}^{3}}\) to \(\frac{64}{{x}^{3}}\).
\[\frac{\frac{64}{{x}^{3}}}{27}\]
Simplify.
\[\frac{64}{27{x}^{3}}\]
64/(27*x^3)
