Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[\frac{{(3xy)}^{2}\sqrt{{x}^{4}}\sqrt{{y}^{6}}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Simplify \(\sqrt{{x}^{4}}\) to \({x}^{2}\).
\[\frac{{(3xy)}^{2}{x}^{2}\sqrt{{y}^{6}}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Simplify \(\sqrt{{y}^{6}}\) to \({y}^{3}\).
\[\frac{{(3xy)}^{2}{x}^{2}{y}^{3}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{3}^{2}{x}^{2}{y}^{2}{x}^{2}{y}^{3}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{9{x}^{2}{y}^{2}{x}^{2}{y}^{3}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Regroup terms.
\[\frac{9{x}^{2}{x}^{2}{y}^{2}{y}^{3}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{9{x}^{2+2}{y}^{2+3}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Simplify \(2+2\) to \(4\).
\[\frac{9{x}^{4}{y}^{2+3}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Simplify \(2+3\) to \(5\).
\[\frac{9{x}^{4}{y}^{5}}{{(2{x}^{4}{y}^{3})}^{-1}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{9{x}^{4}{y}^{5}}{\frac{1}{2{x}^{4}{y}^{3}}}\]
Invert and multiply.
\[9{x}^{4}{y}^{5}\times 2{x}^{4}{y}^{3}\]
Take out the constants.
\[(9\times 2){x}^{4}{x}^{4}{y}^{5}{y}^{3}\]
Simplify \(9\times 2\) to \(18\).
\[18{x}^{4}{x}^{4}{y}^{5}{y}^{3}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[18{x}^{4+4}{y}^{5+3}\]
Simplify \(4+4\) to \(8\).
\[18{x}^{8}{y}^{5+3}\]
Simplify \(5+3\) to \(8\).
\[18{x}^{8}{y}^{8}\]
18*x^8*y^8
