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

(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.
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.
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.
Raise 4 to the power of 2.
a816(b6)2
Multiply the exponents in (b6)2.
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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