What is (2^3a^{-4}b^5)^{-2} ?

The solution to (2^3a^{-4}b^5)^{-2} is (a^8)/(64b^{10)}

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simplify (2^3a^{-4}b^5)^{-2}

simplify

(2^{3} a^{- 4} b^{5})^{- 2}

\frac{a ^{8}}{64 b ^{10}}

Solution steps

(2^{3} a^{- 4} b^{5})^{- 2}

Apply exponent rule:

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

(2^{3} a^{- 4} b^{5})^{- 2} = \frac{1}{( 2 ^{3} a ^{- 4} b ^{5} ) ^{2}}

= \frac{1}{( 2 ^{3} a ^{- 4} b ^{5} ) ^{2}}

Simplify

(2^{3} a^{- 4} b^{5})^{2} : \frac{64 b ^{10}}{a ^{8}}

= \frac{1}{\frac{64 b ^{10}}{a ^{8}}}

Apply the fraction rule:

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

= \frac{a ^{8}}{64 b ^{10}}

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What is (2^3a^{-4}b^5)^{-2} ?
The solution to (2^3a^{-4}b^5)^{-2} is (a^8)/(64b^{10)}