What is the simplified form of ((a^2⁢b^5)^3)/((a⁢b)^−2)÷((a⁢b^−2))/((a^0⁢b)^−2) ?

First simplify the left fraction: (a²b⁵)³ = a⁶b¹⁵ and (ab)⁻² = a⁻²b⁻², so their quotient is a⁸b¹⁷. In the right fraction, (a⁰b)⁻² = b⁻², so ab⁻² divided by b⁻² equals a. Dividing a⁸b¹⁷ by a gives a⁷b¹⁷, which is choice A, “a to the 7th power b to the 17th power.”

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