Simplify (4a^-4b^6)^-2

Math
(4a-4b6)-2
Rewrite the expression using the negative exponent rule b-n=1bn.
(41a4b6)-2
Combine 4 and 1a4.
(4a4b6)-2
Combine 4a4 and b6.
(4b6a4)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(a44b6)2
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to a44b6.
(a4)2(4b6)2
Apply the product rule to 4b6.
(a4)242(b6)2
(a4)242(b6)2
Multiply the exponents in (a4)2.
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Apply the power rule and multiply exponents, (am)n=amn.
a4⋅242(b6)2
Multiply 4 by 2.
a842(b6)2
a842(b6)2
Simplify the denominator.
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Raise 4 to the power of 2.
a816(b6)2
Multiply the exponents in (b6)2.
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Apply the power rule and multiply exponents, (am)n=amn.
a816b6⋅2
Multiply 6 by 2.
a816b12
a816b12
a816b12
Simplify (4a^-4b^6)^-2

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