What is ((2a^{-1}b)/(a^2b^{-3)})^{-3} ?

The solution to ((2a^{-1}b)/(a^2b^{-3)})^{-3} is (a^9)/(8b^{12)}

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simplify ((2a^{-1}b)/(a^2b^{-3)})^{-3}

simplify

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{- 3}

\frac{a ^{9}}{8 b ^{12}}

Solution steps

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{- 3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{- 3} = \frac{1}{( \frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}} ) ^{3}}

= \frac{1}{( \frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}} ) ^{3}}

Simplify

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{3} : \frac{8 b ^{12}}{a ^{9}}

= \frac{1}{\frac{8 b ^{12}}{a ^{9}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{a ^{9}}{8 b ^{12}}

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What is ((2a^{-1}b)/(a^2b^{-3)})^{-3} ?
The solution to ((2a^{-1}b)/(a^2b^{-3)})^{-3} is (a^9)/(8b^{12)}