Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{{3}^{5}\times \frac{1}{{6}^{3}}}{{9}^{2}\times {6}^{-2}}\]
Simplify \({3}^{5}\) to \(243\).
\[\frac{243\times \frac{1}{{6}^{3}}}{{9}^{2}\times {6}^{-2}}\]
Simplify \({6}^{3}\) to \(216\).
\[\frac{243\times \frac{1}{216}}{{9}^{2}\times {6}^{-2}}\]
Simplify \(243\times \frac{1}{216}\) to \(\frac{243}{216}\).
\[\frac{\frac{243}{216}}{{9}^{2}\times {6}^{-2}}\]
Simplify \(\frac{243}{216}\) to \(\frac{9}{8}\).
\[\frac{\frac{9}{8}}{{9}^{2}\times {6}^{-2}}\]
Simplify \({9}^{2}\) to \(81\).
\[\frac{\frac{9}{8}}{81\times {6}^{-2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{9}{8}}{81\times \frac{1}{{6}^{2}}}\]
Simplify \({6}^{2}\) to \(36\).
\[\frac{\frac{9}{8}}{81\times \frac{1}{36}}\]
Simplify \(81\times \frac{1}{36}\) to \(\frac{81}{36}\).
\[\frac{\frac{9}{8}}{\frac{81}{36}}\]
Simplify \(\frac{81}{36}\) to \(\frac{9}{4}\).
\[\frac{\frac{9}{8}}{\frac{9}{4}}\]
Invert and multiply.
\[\frac{9}{8}\times \frac{4}{9}\]
Cancel \(9\).
\[\frac{1}{8}\times 4\]
Simplify.
\[\frac{4}{8}\]
Simplify.
\[\frac{1}{2}\]
Decimal Form: 0.5
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