Simplify \({2}^{6}\) to \(64\).
\[\begin{aligned}&{(64\times {3}^{4}\times {5}^{2})}^{\frac{3}{2}}\\&\sqrt[256]{4}\sqrt{729}\sqrt[125]{3}\end{aligned}\]
Simplify \({3}^{4}\) to \(81\).
\[\begin{aligned}&{(64\times 81\times {5}^{2})}^{\frac{3}{2}}\\&\sqrt[256]{4}\sqrt{729}\sqrt[125]{3}\end{aligned}\]
Simplify \({5}^{2}\) to \(25\).
\[\begin{aligned}&{(64\times 81\times 25)}^{\frac{3}{2}}\\&\sqrt[256]{4}\sqrt{729}\sqrt[125]{3}\end{aligned}\]
Simplify \(64\times 81\) to \(5184\).
\[\begin{aligned}&{(5184\times 25)}^{\frac{3}{2}}\\&\sqrt[256]{4}\sqrt{729}\sqrt[125]{3}\end{aligned}\]
Simplify \(5184\times 25\) to \(129600\).
\[\begin{aligned}&{129600}^{\frac{3}{2}}\\&\sqrt[256]{4}\sqrt{729}\sqrt[125]{3}\end{aligned}\]
Since \(27\times 27=729\), the square root of \(729\) is \(27\).
\[\begin{aligned}&{129600}^{\frac{3}{2}}\\&\sqrt[256]{4}\times 27\sqrt[125]{3}\end{aligned}\]
129600^(3/2);4^(1/256)*27*3^(1/125)
