Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{{4}^{6}}{{5}^{6}}{}^{{(\frac{3}{2})}^{6}}\]
Simplify \({4}^{6}\) to \(4096\).
\[\frac{4096}{{5}^{6}}{}^{{(\frac{3}{2})}^{6}}\]
Simplify \({5}^{6}\) to \(15625\).
\[\frac{4096}{15625}{}^{{(\frac{3}{2})}^{6}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{4096}{15625}{}^{\frac{{3}^{6}}{{2}^{6}}}\]
Simplify \({3}^{6}\) to \(729\).
\[\frac{4096}{15625}{}^{\frac{729}{{2}^{6}}}\]
Simplify \({2}^{6}\) to \(64\).
\[\frac{4096}{15625}{}^{\frac{729}{64}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{4096{}^{\frac{729}{64}}}{15625}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{4096{}^{\frac{793}{64}}}{15625}\]
(4096*^(793/64))/15625
