Simplify (6ab^2)(12ab^-2)^-1

(6ab2)(12ab-2)-1

Rewrite the expression using the negative exponent rule b-n=1bn.

6ab2(12a1b2)-1

Multiply 12a1b2.

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Combine 12 and 1b2.

6ab2(a12b2)-1

Combine a and 12b2.

6ab2(a⋅12b2)-1

Move 12 to the left of a.

6ab2(12⋅ab2)-1

Change the sign of the exponent by rewriting the base as its reciprocal.

6ab2b212a

Cancel the common factor of 6a.

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Factor 6a out of 6ab2.

6a(b2)b212a

Factor 6a out of 12a.

6a(b2)b26a(2)

Cancel the common factor.

6ab2b26a⋅2

Rewrite the expression.

b2b22

Combine b2 and b22.

b2b22

Multiply b2 by b2 by adding the exponents.

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Use the power rule aman=am+n to combine exponents.

b2+22

Add 2 and 2.

b42

Simplify (6ab^2)(12ab^-2)^-1