What is ((5a^{-5})/(3b^{-1/6)})^{-1} ?

The solution to ((5a^{-5})/(3b^{-1/6)})^{-1} is (3a^5)/(5b^{1/6)}

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simplify ((5a^{-5})/(3b^{-1/6)})^{-1}

simplify

(\frac{5 a ^{- 5}}{3 b ^{- \frac{1}{6}}})^{- 1}

\frac{3 a ^{5}}{5 b ^{\frac{1}{6}}}

Solution steps

(\frac{5 a ^{- 5}}{3 b ^{- \frac{1}{6}}})^{- 1}

Apply exponent rule:

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

(\frac{5 a ^{- 5}}{3 b ^{- \frac{1}{6}}})^{- 1} = \frac{1}{\frac{5 a ^{- 5}}{3 b ^{- \frac{1}{6}}}}

= \frac{1}{\frac{5 a ^{- 5}}{3 b ^{- \frac{1}{6}}}}

Apply the fraction rule:

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

= \frac{3 b ^{- \frac{1}{6}}}{5 a ^{- 5}}

Multiply

3 b^{- \frac{1}{6}} : \frac{3}{b ^{\frac{1}{6}}}

= \frac{\frac{3}{b ^{\frac{1}{6}}}}{5 a ^{- 5}}

Apply the fraction rule:

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

= \frac{3}{b ^{\frac{1}{6}} \cdot 5 a ^{- 5}}

a^{- 5} = \frac{1}{a ^{5}}

= \frac{3}{5 \cdot \frac{1}{a ^{5}} b ^{\frac{1}{6}}}

Multiply

b^{\frac{1}{6}} \cdot 5 \cdot \frac{1}{a ^{5}} : \frac{5 b ^{\frac{1}{6}}}{a ^{5}}

= \frac{3}{\frac{5 b ^{\frac{1}{6}}}{a ^{5}}}

Apply the fraction rule:

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

= \frac{3 a ^{5}}{5 b ^{\frac{1}{6}}}

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What is ((5a^{-5})/(3b^{-1/6)})^{-1} ?
The solution to ((5a^{-5})/(3b^{-1/6)})^{-1} is (3a^5)/(5b^{1/6)}