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

The solution to (a^2*a^{-5})^{-3}*(a*a^3)^4 is a^{25}

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

simplify

(a^{2} \cdot a^{- 5})^{- 3} \cdot (a \cdot a^{3})^{4}

a^{25}

Solution steps

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

Simplify

(a^{2} a^{- 5})^{- 3} : a^{9}

= a^{9} (a a^{3})^{4}

Simplify

(a a^{3})^{4} : a^{16}

= a^{9} a^{16}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

a^{9} a^{16} = a^{9 + 16}

= a^{9 + 16}

Add the numbers:

9 + 16 = 25

= a^{25}

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What is (a^2*a^{-5})^{-3}*(a*a^3)^4 ?
The solution to (a^2*a^{-5})^{-3}*(a*a^3)^4 is a^{25}