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

(2ab6a3b)-2

Cancel the common factor of a and a3.

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Factor a out of 2ab6.

(a(2b6)a3b)-2

Cancel the common factors.

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Factor a out of a3b.

(a(2b6)a(a2b))-2

Cancel the common factor.

(a(2b6)a(a2b))-2

Rewrite the expression.

(2b6a2b)-2

Cancel the common factor of b6 and b.

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Factor b out of 2b6.

(b(2b5)a2b)-2

Cancel the common factors.

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Factor b out of a2b.

(b(2b5)ba2)-2

Cancel the common factor.

(b(2b5)ba2)-2

Rewrite the expression.

(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.

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Apply the product rule to a22b5.

(a2)2(2b5)2

Apply the product rule to 2b5.

(a2)222(b5)2

Multiply the exponents in (a2)2.

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Apply the power rule and multiply exponents, (am)n=amn.

a2⋅222(b5)2

Multiply 2 by 2.

a422(b5)2

Simplify the denominator.

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Raise 2 to the power of 2.

a44(b5)2

Multiply the exponents in (b5)2.

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Apply the power rule and multiply exponents, (am)n=amn.

a44b5⋅2

Multiply 5 by 2.

a44b10

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

Solving MATH problems