Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{{(\frac{1}{2})}^{8}}{(\frac{2}{3})}^{-2}{(\frac{9}{4})}^{3}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{\frac{1}{{2}^{8}}}{(\frac{2}{3})}^{-2}{(\frac{9}{4})}^{3}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \({2}^{8}\) to \(256\).
\[\frac{\frac{1}{\frac{1}{256}}{(\frac{2}{3})}^{-2}{(\frac{9}{4})}^{3}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{\frac{1}{256}}\times \frac{1}{{(\frac{2}{3})}^{2}}{(\frac{9}{4})}^{3}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{{2}^{2}}{{3}^{2}}}{(\frac{9}{4})}^{3}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \({2}^{2}\) to \(4\).
\[\frac{\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{{3}^{2}}}{(\frac{9}{4})}^{3}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}\times \frac{{9}^{3}}{{4}^{3}}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \({9}^{3}\) to \(729\).
\[\frac{\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}\times \frac{729}{{4}^{3}}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \({4}^{3}\) to \(64\).
\[\frac{\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}\times \frac{729}{64}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Invert and multiply.
\[\frac{256\times \frac{1}{\frac{4}{9}}\times \frac{729}{64}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\frac{256\times 1\times 729}{\frac{4}{9}\times 64}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \(256\times 1\) to \(256\).
\[\frac{\frac{256\times 729}{\frac{4}{9}\times 64}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \(256\times 729\) to \(186624\).
\[\frac{\frac{186624}{\frac{4}{9}\times 64}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{\frac{186624}{\frac{4\times 64}{9}}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \(4\times 64\) to \(256\).
\[\frac{\frac{186624}{\frac{256}{9}}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Invert and multiply.
\[\frac{186624\times \frac{9}{256}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{\frac{186624\times 9}{256}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \(186624\times 9\) to \(1679616\).
\[\frac{\frac{1679616}{256}}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \(\frac{1679616}{256}\) to \(6561\).
\[\frac{6561}{{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Simplify \({2}^{3}\) to \(8\).
\[\frac{6561}{8{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{6561}{8\times \frac{1}{\frac{4}{9}}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{6561}{8\times \frac{1}{\frac{4}{9}}\times \frac{1}{{(\frac{1}{3})}^{3}}{(\frac{4}{3})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{6561}{8\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{{3}^{3}}}{(\frac{4}{3})}^{2}}\]
Simplify \({3}^{3}\) to \(27\).
\[\frac{6561}{8\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}{(\frac{4}{3})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{6561}{8\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}\times \frac{{4}^{2}}{{3}^{2}}}\]
Simplify \({4}^{2}\) to \(16\).
\[\frac{6561}{8\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}\times \frac{16}{{3}^{2}}}\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{6561}{8\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}\times \frac{16}{9}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{6561}{\frac{8\times 1\times 1\times 16}{\frac{4}{9}\times \frac{1}{27}\times 9}}\]
Simplify \(8\times 1\) to \(8\).
\[\frac{6561}{\frac{8\times 1\times 16}{\frac{4}{9}\times \frac{1}{27}\times 9}}\]
Simplify \(8\times 1\) to \(8\).
\[\frac{6561}{\frac{8\times 16}{\frac{4}{9}\times \frac{1}{27}\times 9}}\]
Simplify \(8\times 16\) to \(128\).
\[\frac{6561}{\frac{128}{\frac{4}{9}\times \frac{1}{27}\times 9}}\]
Cancel \(9\).
\[\frac{6561}{\frac{128}{4\times \frac{1}{27}}}\]
Simplify \(4\times \frac{1}{27}\) to \(\frac{4}{27}\).
\[\frac{6561}{\frac{128}{\frac{4}{27}}}\]
Invert and multiply.
\[\frac{6561}{128\times \frac{27}{4}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{6561}{\frac{128\times 27}{4}}\]
Simplify \(128\times 27\) to \(3456\).
\[\frac{6561}{\frac{3456}{4}}\]
Simplify \(\frac{3456}{4}\) to \(864\).
\[\frac{6561}{864}\]
Simplify.
\[\frac{243}{32}\]
Decimal Form: 7.59375
243/32
