# Simplify ((6a^2b^-2)/(2ab^-1))^-2

(6a2b-22ab-1)-2
Move b-2 to the denominator using the negative exponent rule b-n=1bn.
(6a22ab-1b2)-2
Simplify the denominator.
Multiply b-1 by b2 by adding the exponents.
Move b2.
(6a22a(b2b-1))-2
Use the power rule aman=am+n to combine exponents.
(6a22ab2-1)-2
Subtract 1 from 2.
(6a22ab1)-2
(6a22ab1)-2
Simplify 2ab1.
(6a22ab)-2
(6a22ab)-2
Cancel the common factor of 6 and 2.
Factor 2 out of 6a2.
(2(3a2)2ab)-2
Cancel the common factors.
Factor 2 out of 2ab.
(2(3a2)2(ab))-2
Cancel the common factor.
(2(3a2)2(ab))-2
Rewrite the expression.
(3a2ab)-2
(3a2ab)-2
(3a2ab)-2
Cancel the common factor of a2 and a.
Factor a out of 3a2.
(a(3a)ab)-2
Cancel the common factors.
Factor a out of ab.
(a(3a)a(b))-2
Cancel the common factor.
(a(3a)ab)-2
Rewrite the expression.
(3ab)-2
(3ab)-2
(3ab)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(b3a)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to b3a.
b2(3a)2
Apply the product rule to 3a.
b232a2
b232a2
Raise 3 to the power of 2.
b29a2
Simplify ((6a^2b^-2)/(2ab^-1))^-2

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