Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{{2}^{5}}{{3}^{5}}{(\frac{2}{3})}^{7}\]
Simplify \({2}^{5}\) to \(32\).
\[\frac{32}{{3}^{5}}{(\frac{2}{3})}^{7}\]
Simplify \({3}^{5}\) to \(243\).
\[\frac{32}{243}{(\frac{2}{3})}^{7}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{32}{243}\times \frac{{2}^{7}}{{3}^{7}}\]
Simplify \({2}^{7}\) to \(128\).
\[\frac{32}{243}\times \frac{128}{{3}^{7}}\]
Simplify \({3}^{7}\) to \(2187\).
\[\frac{32}{243}\times \frac{128}{2187}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{32\times 128}{243\times 2187}\]
Simplify \(32\times 128\) to \(4096\).
\[\frac{4096}{243\times 2187}\]
Simplify \(243\times 2187\) to \(531441\).
\[\frac{4096}{531441}\]
Decimal Form: 0.007707
4096/531441
