Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{{(\frac{25}{9})}^{\frac{3}{5}}}}{{(\frac{5}{2})}^{-3}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{\frac{{25}^{\frac{3}{5}}}{{9}^{\frac{3}{5}}}}}{{(\frac{5}{2})}^{-3}}\]
Rewrite \(25\) as \({5}^{2}\).
\[\frac{\frac{1}{\frac{{({5}^{2})}^{\frac{3}{5}}}{{9}^{\frac{3}{5}}}}}{{(\frac{5}{2})}^{-3}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{1}{\frac{{5}^{\frac{2\times 3}{5}}}{{9}^{\frac{3}{5}}}}}{{(\frac{5}{2})}^{-3}}\]
Simplify \(2\times 3\) to \(6\).
\[\frac{\frac{1}{\frac{{5}^{\frac{6}{5}}}{{9}^{\frac{3}{5}}}}}{{(\frac{5}{2})}^{-3}}\]
Rewrite \(9\) as \({3}^{2}\).
\[\frac{\frac{1}{\frac{{5}^{\frac{6}{5}}}{{({3}^{2})}^{\frac{3}{5}}}}}{{(\frac{5}{2})}^{-3}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{1}{\frac{{5}^{\frac{6}{5}}}{{3}^{\frac{2\times 3}{5}}}}}{{(\frac{5}{2})}^{-3}}\]
Simplify \(2\times 3\) to \(6\).
\[\frac{\frac{1}{\frac{{5}^{\frac{6}{5}}}{{3}^{\frac{6}{5}}}}}{{(\frac{5}{2})}^{-3}}\]
Invert and multiply.
\[\frac{\frac{{3}^{\frac{6}{5}}}{{5}^{\frac{6}{5}}}}{{(\frac{5}{2})}^{-3}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{{3}^{\frac{6}{5}}}{{5}^{\frac{6}{5}}}}{\frac{1}{{(\frac{5}{2})}^{3}}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{{3}^{\frac{6}{5}}}{{5}^{\frac{6}{5}}}}{\frac{1}{\frac{{5}^{3}}{{2}^{3}}}}\]
Simplify \({5}^{3}\) to \(125\).
\[\frac{\frac{{3}^{\frac{6}{5}}}{{5}^{\frac{6}{5}}}}{\frac{1}{\frac{125}{{2}^{3}}}}\]
Simplify \({2}^{3}\) to \(8\).
\[\frac{\frac{{3}^{\frac{6}{5}}}{{5}^{\frac{6}{5}}}}{\frac{1}{\frac{125}{8}}}\]
Invert and multiply.
\[\frac{\frac{{3}^{\frac{6}{5}}}{{5}^{\frac{6}{5}}}}{\frac{8}{125}}\]
Invert and multiply.
\[\frac{{3}^{\frac{6}{5}}}{{5}^{\frac{6}{5}}}\times \frac{125}{8}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{{3}^{\frac{6}{5}}\times 125}{{5}^{\frac{6}{5}}\times 8}\]
Decimal Form: 8.464504
(3^(6/5)*125)/(5^(6/5)*8)
