Rewrite \(216\) as \({6}^{3}\).
\[Simpl\imath fy\sqrt{\frac{{({6}^{3})}^{\frac{2}{3}}\times {25}^{\frac{1}{2}}}{{0.04}^{-\frac{1}{2}}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[Simpl\imath fy\sqrt{\frac{{6}^{\frac{3\times 2}{3}}\times {25}^{\frac{1}{2}}}{{0.04}^{-\frac{1}{2}}}}\]
Simplify \(3\times 2\) to \(6\).
\[Simpl\imath fy\sqrt{\frac{{6}^{\frac{6}{3}}\times {25}^{\frac{1}{2}}}{{0.04}^{-\frac{1}{2}}}}\]
Simplify \(\frac{6}{3}\) to \(2\).
\[Simpl\imath fy\sqrt{\frac{{6}^{2}\times {25}^{\frac{1}{2}}}{{0.04}^{-\frac{1}{2}}}}\]
Simplify \({6}^{2}\) to \(36\).
\[Simpl\imath fy\sqrt{\frac{36\times {25}^{\frac{1}{2}}}{{0.04}^{-\frac{1}{2}}}}\]
Convert \({25}^{\frac{1}{2}}\) to square root.
\[Simpl\imath fy\sqrt{\frac{36\sqrt{25}}{{0.04}^{-\frac{1}{2}}}}\]
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[Simpl\imath fy\sqrt{\frac{36\times 5}{{0.04}^{-\frac{1}{2}}}}\]
Simplify \(36\times 5\) to \(180\).
\[Simpl\imath fy\sqrt{\frac{180}{{0.04}^{-\frac{1}{2}}}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[Simpl\imath fy\sqrt{\frac{180}{\frac{1}{\sqrt{0.04}}}}\]
Simplify \(\sqrt{0.04}\) to \(0.2\).
\[Simpl\imath fy\sqrt{\frac{180}{\frac{1}{0.2}}}\]
Simplify \(\frac{1}{0.2}\) to \(5\).
\[Simpl\imath fy\sqrt{\frac{180}{5}}\]
Simplify \(\frac{180}{5}\) to \(36\).
\[Simpl\imath fy\sqrt{36}\]
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[Simpl\imath fy\times 6\]
Regroup terms.
\[6Si\imath mplfy\]
6*Si*IM*m*p*l*f*y
