Remove parentheses.
\[\sqrt{\frac{{216}^{\frac{2}{3}}{({}^{125})}^{2}}{{0.04}^{-3}}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\sqrt{\frac{{216}^{\frac{2}{3}}{({}^{125}{}^{125})}^{2}}{{0.04}^{-3}}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\sqrt{\frac{{216}^{\frac{2}{3}}{}^{{250}^{2}}}{{0.04}^{-3}}}\]
Rewrite \(216\) as \({6}^{3}\).
\[\sqrt{\frac{{({6}^{3})}^{\frac{2}{3}}{}^{{250}^{2}}}{{0.04}^{-3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\sqrt{\frac{{6}^{\frac{3\times 2}{3}}{}^{{250}^{2}}}{{0.04}^{-3}}}\]
Simplify \(3\times 2\) to \(6\).
\[\sqrt{\frac{{6}^{\frac{6}{3}}{}^{{250}^{2}}}{{0.04}^{-3}}}\]
Simplify \(\frac{6}{3}\) to \(2\).
\[\sqrt{\frac{{6}^{2}{}^{{250}^{2}}}{{0.04}^{-3}}}\]
Simplify \({6}^{2}\) to \(36\).
\[\sqrt{\frac{36{}^{{250}^{2}}}{{0.04}^{-3}}}\]
Simplify \({250}^{2}\) to \(62500\).
\[\sqrt{\frac{36{}^{62500}}{{0.04}^{-3}}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\sqrt{\frac{36{}^{62500}}{\frac{1}{{0.04}^{3}}}}\]
Simplify \({0.04}^{3}\) to \(6.4\times {10}^{-5}\).
\[\sqrt{\frac{36{}^{62500}}{\frac{1}{6.4\times {10}^{-5}}}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\sqrt{\frac{36{}^{62500}}{\frac{1}{6.4\times \frac{1}{{10}^{5}}}}}\]
Simplify \({10}^{5}\) to \(100000\).
\[\sqrt{\frac{36{}^{62500}}{\frac{1}{6.4\times \frac{1}{100000}}}}\]
Simplify \(6.4\times \frac{1}{100000}\) to \(6.4\times {10}^{-5}\).
\[\sqrt{\frac{36{}^{62500}}{\frac{1}{6.4\times {10}^{-5}}}}\]
sqrt((36*^62500)/(1/(6.4*10^-5)))
