Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\sqrt[3]{\frac{1}{{5}^{3}}\times {3}^{6}}\times 4\sqrt{16}}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Simplify \({5}^{3}\) to \(125\).
\[\frac{\sqrt[3]{\frac{1}{125}\times {3}^{6}}\times 4\sqrt{16}}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Simplify \({3}^{6}\) to \(729\).
\[\frac{\sqrt[3]{\frac{1}{125}\times 729}\times 4\sqrt{16}}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Simplify \(\frac{1}{125}\times 729\) to \(\frac{729}{125}\).
\[\frac{\sqrt[3]{\frac{729}{125}}\times 4\sqrt{16}}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[\frac{\sqrt[3]{\frac{729}{125}}\times 4\times 4}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{\sqrt[3]{729}}{\sqrt[3]{125}}\times 4\times 4}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Calculate.
\[\frac{\frac{9}{\sqrt[3]{125}}\times 4\times 4}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Calculate.
\[\frac{\frac{9}{5}\times 4\times 4}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\frac{9\times 4\times 4}{5}}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Simplify \(9\times 4\) to \(36\).
\[\frac{\frac{36\times 4}{5}}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Simplify \(36\times 4\) to \(144\).
\[\frac{\frac{144}{5}}{{(125\times 729\times 64)}^{-\frac{1}{3}}}\]
Simplify \(125\times 729\) to \(91125\).
\[\frac{\frac{144}{5}}{{(91125\times 64)}^{-\frac{1}{3}}}\]
Simplify \(91125\times 64\) to \(5832000\).
\[\frac{\frac{144}{5}}{{5832000}^{-\frac{1}{3}}}\]
Calculate.
\[\frac{\frac{144}{5}}{{180}^{-1}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{144}{5}}{\frac{1}{180}}\]
Invert and multiply.
\[\frac{144}{5}\times 180\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{144\times 180}{5}\]
Simplify \(144\times 180\) to \(25920\).
\[\frac{25920}{5}\]
Simplify.
\[5184\]
5184
