# Simplify ((a^3)/(a^-2b))^2*((ab^-2)/(b^2))^-2

(a3a-2b)2⋅(ab-2b2)-2
Move a-2 to the numerator using the negative exponent rule 1b-n=bn.
(a3a2b)2⋅(ab-2b2)-2
Multiply a3 by a2 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
(a3+2b)2⋅(ab-2b2)-2
(a5b)2⋅(ab-2b2)-2
(a5b)2⋅(ab-2b2)-2
Apply the product rule to a5b.
(a5)2b2⋅(ab-2b2)-2
Multiply the exponents in (a5)2.
Apply the power rule and multiply exponents, (am)n=amn.
a5⋅2b2⋅(ab-2b2)-2
Multiply 5 by 2.
a10b2⋅(ab-2b2)-2
a10b2⋅(ab-2b2)-2
Move b-2 to the denominator using the negative exponent rule b-n=1bn.
a10b2⋅(ab2b2)-2
Multiply b2 by b2 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
a10b2⋅(ab2+2)-2
a10b2⋅(ab4)-2
a10b2⋅(ab4)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
a10b2⋅(b4a)2
Apply basic rules of exponents.
Apply the product rule to b4a.
a10b2⋅(b4)2a2
Multiply the exponents in (b4)2.
Apply the power rule and multiply exponents, (am)n=amn.
a10b2⋅b4⋅2a2
Multiply 4 by 2.
a10b2⋅b8a2
a10b2⋅b8a2
a10b2⋅b8a2
Cancel the common factor of a2.
Factor a2 out of a10.
a2a8b2⋅b8a2
Cancel the common factor.
a2a8b2⋅b8a2
Rewrite the expression.
a8b2⋅b8
a8b2⋅b8
Cancel the common factor of b2.
Factor b2 out of b8.
a8b2⋅(b2b6)
Cancel the common factor.
a8b2⋅(b2b6)
Rewrite the expression.
a8⋅b6
a8b6
Simplify ((a^3)/(a^-2b))^2*((ab^-2)/(b^2))^-2

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