What is ((a^5b^{-13})/(2a^{-5)b^{-8}})^{-2} ?

The solution to ((a^5b^{-13})/(2a^{-5)b^{-8}})^{-2} is (4b^{10})/(a^{20)}

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simplify ((a^5b^{-13})/(2a^{-5)b^{-8}})^{-2}

simplify

(\frac{a ^{5} b ^{- 13}}{2 a ^{- 5} b ^{- 8}})^{- 2}

\frac{4 b ^{10}}{a ^{20}}

Solution steps

(\frac{a ^{5} b ^{- 13}}{2 a ^{- 5} b ^{- 8}})^{- 2}

Apply exponent rule:

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

(\frac{a ^{5} b ^{- 13}}{2 a ^{- 5} b ^{- 8}})^{- 2} = \frac{1}{( \frac{a ^{5} b ^{- 13}}{2 a ^{- 5} b ^{- 8}} ) ^{2}}

= \frac{1}{( \frac{a ^{5} b ^{- 13}}{2 a ^{- 5} b ^{- 8}} ) ^{2}}

Simplify

(\frac{a ^{5} b ^{- 13}}{2 a ^{- 5} b ^{- 8}})^{2} : \frac{a ^{20}}{4 b ^{10}}

= \frac{1}{\frac{a ^{20}}{4 b ^{10}}}

Apply the fraction rule:

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

= \frac{4 b ^{10}}{a ^{20}}

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What is ((a^5b^{-13})/(2a^{-5)b^{-8}})^{-2} ?
The solution to ((a^5b^{-13})/(2a^{-5)b^{-8}})^{-2} is (4b^{10})/(a^{20)}