Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{3}^{2}{x}^{2}{(2y)}^{3}{(2xy)}^{2}}{{(2xy)}^{3}}\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{9{x}^{2}{(2y)}^{3}{(2xy)}^{2}}{{(2xy)}^{3}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{9{x}^{2}\times {2}^{3}{y}^{3}{(2xy)}^{2}}{{(2xy)}^{3}}\]
Simplify \({2}^{3}\) to \(8\).
\[\frac{9{x}^{2}\times 8{y}^{3}{(2xy)}^{2}}{{(2xy)}^{3}}\]
Simplify \(9{x}^{2}\times 8{y}^{3}{(2xy)}^{2}\) to \(72{x}^{2}{y}^{3}{(2xy)}^{2}\).
\[\frac{72{x}^{2}{y}^{3}{(2xy)}^{2}}{{(2xy)}^{3}}\]
Simplify.
\[\frac{72{x}^{2}{y}^{3}}{2xy}\]
Take out the constants.
\[\frac{72}{2}\times \frac{{x}^{2}{y}^{3}}{xy}\]
Simplify \(\frac{72}{2}\) to \(36\).
\[36\times \frac{{x}^{2}{y}^{3}}{xy}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[36{x}^{2-1}{y}^{3-1}\]
Simplify \(2-1\) to \(1\).
\[36{x}^{1}{y}^{3-1}\]
Simplify \(3-1\) to \(2\).
\[36{x}^{1}{y}^{2}\]
Use Rule of One: \({x}^{1}=x\).
\[36x{y}^{2}\]
36*x*y^2
