# Simplify ((2ab^6)/(a^3b))^-2

(2ab6a3b)-2
Cancel the common factor of a and a3.
Factor a out of 2ab6.
(a(2b6)a3b)-2
Cancel the common factors.
Factor a out of a3b.
(a(2b6)a(a2b))-2
Cancel the common factor.
(a(2b6)a(a2b))-2
Rewrite the expression.
(2b6a2b)-2
(2b6a2b)-2
(2b6a2b)-2
Cancel the common factor of b6 and b.
Factor b out of 2b6.
(b(2b5)a2b)-2
Cancel the common factors.
Factor b out of a2b.
(b(2b5)ba2)-2
Cancel the common factor.
(b(2b5)ba2)-2
Rewrite the expression.
(2b5a2)-2
(2b5a2)-2
(2b5a2)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(a22b5)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to a22b5.
(a2)2(2b5)2
Apply the product rule to 2b5.
(a2)222(b5)2
(a2)222(b5)2
Multiply the exponents in (a2)2.
Apply the power rule and multiply exponents, (am)n=amn.
a2⋅222(b5)2
Multiply 2 by 2.
a422(b5)2
a422(b5)2
Simplify the denominator.
Raise 2 to the power of 2.
a44(b5)2
Multiply the exponents in (b5)2.
Apply the power rule and multiply exponents, (am)n=amn.
a44b5⋅2
Multiply 5 by 2.
a44b10
a44b10
a44b10
Simplify ((2ab^6)/(a^3b))^-2

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