Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{m}^{3}{({n}^{2})}^{3}{\sqrt{mn}}^{4}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{m}^{3}{n}^{6}{\sqrt{mn}}^{4}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{m}^{3}{n}^{6}{(mn)}^{\frac{4}{2}}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Simplify \(\frac{4}{2}\) to \(2\).
\[\frac{{m}^{3}{n}^{6}{(mn)}^{2}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{m}^{3}{n}^{6}{m}^{2}{n}^{2}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Regroup terms.
\[\frac{{m}^{3}{m}^{2}{n}^{6}{n}^{2}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{m}^{3+2}{n}^{6+2}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Simplify \(3+2\) to \(5\).
\[\frac{{m}^{5}{n}^{6+2}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Simplify \(6+2\) to \(8\).
\[\frac{{m}^{5}{n}^{8}}{{({m}^{6}{n}^{3})}^{\frac{2}{3}}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{m}^{5}{n}^{8}}{{({m}^{6})}^{\frac{2}{3}}{({n}^{3})}^{\frac{2}{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{m}^{5}{n}^{8}}{{m}^{\frac{6\times 2}{3}}{({n}^{3})}^{\frac{2}{3}}}\]
Simplify \(6\times 2\) to \(12\).
\[\frac{{m}^{5}{n}^{8}}{{m}^{\frac{12}{3}}{({n}^{3})}^{\frac{2}{3}}}\]
Simplify \(\frac{12}{3}\) to \(4\).
\[\frac{{m}^{5}{n}^{8}}{{m}^{4}{({n}^{3})}^{\frac{2}{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{m}^{5}{n}^{8}}{{m}^{4}{n}^{\frac{3\times 2}{3}}}\]
Simplify \(3\times 2\) to \(6\).
\[\frac{{m}^{5}{n}^{8}}{{m}^{4}{n}^{\frac{6}{3}}}\]
Simplify \(\frac{6}{3}\) to \(2\).
\[\frac{{m}^{5}{n}^{8}}{{m}^{4}{n}^{2}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{m}^{5-4}{n}^{8-2}\]
Simplify \(5-4\) to \(1\).
\[{m}^{1}{n}^{8-2}\]
Simplify \(8-2\) to \(6\).
\[{m}^{1}{n}^{6}\]
Use Rule of One: \({x}^{1}=x\).
\[m{n}^{6}\]
m*n^6
