What is ((3a^{-2})/(4b^{-1/3)})^{-1} ?

The solution to ((3a^{-2})/(4b^{-1/3)})^{-1} is (4a^2)/(3b^{1/3)}

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simplify ((3a^{-2})/(4b^{-1/3)})^{-1}

simplify

(\frac{3 a ^{- 2}}{4 b ^{- \frac{1}{3}}})^{- 1}

\frac{4 a ^{2}}{3 b ^{\frac{1}{3}}}

Solution steps

(\frac{3 a ^{- 2}}{4 b ^{- \frac{1}{3}}})^{- 1}

Apply exponent rule:

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

(\frac{3 a ^{- 2}}{4 b ^{- \frac{1}{3}}})^{- 1} = \frac{1}{\frac{3 a ^{- 2}}{4 b ^{- \frac{1}{3}}}}

= \frac{1}{\frac{3 a ^{- 2}}{4 b ^{- \frac{1}{3}}}}

Apply the fraction rule:

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

= \frac{4 b ^{- \frac{1}{3}}}{3 a ^{- 2}}

Multiply

4 b^{- \frac{1}{3}} : \frac{4}{b ^{\frac{1}{3}}}

= \frac{\frac{4}{b ^{\frac{1}{3}}}}{3 a ^{- 2}}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{4}{b ^{\frac{1}{3}} \cdot 3 a ^{- 2}}

a^{- 2} = \frac{1}{a ^{2}}

= \frac{4}{3 \cdot \frac{1}{a ^{2}} b ^{\frac{1}{3}}}

Multiply

b^{\frac{1}{3}} \cdot 3 \cdot \frac{1}{a ^{2}} : \frac{3 b ^{\frac{1}{3}}}{a ^{2}}

= \frac{4}{\frac{3 b ^{\frac{1}{3}}}{a ^{2}}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{4 a ^{2}}{3 b ^{\frac{1}{3}}}

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What is ((3a^{-2})/(4b^{-1/3)})^{-1} ?
The solution to ((3a^{-2})/(4b^{-1/3)})^{-1} is (4a^2)/(3b^{1/3)}