Cancel \(2\).
\[\sqrt{\frac{{216}^{\frac{2}{3}}{}^{{125}^{1}}}{{0.04}^{\frac{-3}{2}}}}\]
Rewrite \(216\) as \({6}^{3}\).
\[\sqrt{\frac{{({6}^{3})}^{\frac{2}{3}}{}^{{125}^{1}}}{{0.04}^{\frac{-3}{2}}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\sqrt{\frac{{6}^{\frac{3\times 2}{3}}{}^{{125}^{1}}}{{0.04}^{\frac{-3}{2}}}}\]
Simplify \(3\times 2\) to \(6\).
\[\sqrt{\frac{{6}^{\frac{6}{3}}{}^{{125}^{1}}}{{0.04}^{\frac{-3}{2}}}}\]
Simplify \(\frac{6}{3}\) to \(2\).
\[\sqrt{\frac{{6}^{2}{}^{{125}^{1}}}{{0.04}^{\frac{-3}{2}}}}\]
Simplify \({6}^{2}\) to \(36\).
\[\sqrt{\frac{36{}^{{125}^{1}}}{{0.04}^{\frac{-3}{2}}}}\]
Use Rule of One: \({x}^{1}=x\).
\[\sqrt{\frac{36{}^{125}}{{0.04}^{\frac{-3}{2}}}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\sqrt{\frac{36{}^{126}}{{0.04}^{\frac{-3}{2}}}}\]
Move the negative sign to the left.
\[\sqrt{\frac{36{}^{126}}{{0.04}^{-\frac{3}{2}}}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\sqrt{\frac{36{}^{126}}{\frac{1}{{0.04}^{\frac{3}{2}}}}}\]
Invert and multiply.
\[\sqrt{36{}^{126}\times {0.04}^{\frac{3}{2}}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[\sqrt{36}\sqrt{{}^{126}}\sqrt{{0.04}^{\frac{3}{2}}}\]
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[6\sqrt{{}^{126}}\sqrt{{0.04}^{\frac{3}{2}}}\]
Simplify \(\sqrt{{}^{126}}\) to \({}^{63}\).
\[6{}^{63}\sqrt{{0.04}^{\frac{3}{2}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[6{}^{63}\times {0.04}^{\frac{3\times 1}{2\times 2}}\]
Simplify \(3\times 1\) to \(3\).
\[6{}^{63}\times {0.04}^{\frac{3}{2\times 2}}\]
Simplify \(2\times 2\) to \(4\).
\[6{}^{63}\times {0.04}^{\frac{3}{4}}\]
6*^63*0.04^(3/4)
