Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\begin{aligned}&\frac{1}{{(\frac{1}{2})}^{8}}{(\frac{2}{3})}^{-2}{(\frac{9}{4})}^{3}\\&{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\begin{aligned}&\frac{1}{\frac{1}{{2}^{8}}}{(\frac{2}{3})}^{-2}{(\frac{9}{4})}^{3}\\&{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Simplify \({2}^{8}\) to \(256\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}{(\frac{2}{3})}^{-2}{(\frac{9}{4})}^{3}\\&{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{{(\frac{2}{3})}^{2}}{(\frac{9}{4})}^{3}\\&{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{{2}^{2}}{{3}^{2}}}{(\frac{9}{4})}^{3}\\&{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Simplify \({2}^{2}\) to \(4\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{{3}^{2}}}{(\frac{9}{4})}^{3}\\&{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Simplify \({3}^{2}\) to \(9\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}{(\frac{4}{9})}^{-1}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}{(\frac{1}{3})}^{-3}{(\frac{4}{3})}^{2}\end{aligned}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}\times \frac{1}{{(\frac{1}{3})}^{3}}{(\frac{4}{3})}^{2}\end{aligned}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{{3}^{3}}}{(\frac{4}{3})}^{2}\end{aligned}\]
Simplify \({3}^{3}\) to \(27\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}{(\frac{4}{3})}^{2}\end{aligned}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}\times \frac{{4}^{2}}{{3}^{2}}\end{aligned}\]
Simplify \({4}^{2}\) to \(16\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}\times \frac{16}{{3}^{2}}\end{aligned}\]
Simplify \({3}^{2}\) to \(9\).
\[\begin{aligned}&\frac{1}{\frac{1}{256}}\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}\times \frac{16}{9}\end{aligned}\]
Invert and multiply.
\[\begin{aligned}&256\times \frac{1}{\frac{4}{9}}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{1}{\frac{4}{9}}\times \frac{1}{\frac{1}{27}}\times \frac{16}{9}\end{aligned}\]
Invert and multiply.
\[\begin{aligned}&256\times \frac{9}{4}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{9}{4}\times \frac{1}{\frac{1}{27}}\times \frac{16}{9}\end{aligned}\]
Invert and multiply.
\[\begin{aligned}&256\times \frac{9}{4}{(\frac{9}{4})}^{3}\\&{2}^{3}\times \frac{9}{4}\times 27\times \frac{16}{9}\end{aligned}\]
256*9/4*(9/4)^3;2^3*9/4*27*16/9
