# Simplify ((3a^-1b^4)/(5b^-4a^-6))^-2

(3a-1b45b-4a-6)-2
Move a-6 to the numerator using the negative exponent rule 1b-n=bn.
(3a-1b4a65b-4)-2
Move b-4 to the numerator using the negative exponent rule 1b-n=bn.
(3a-1b4a6b45)-2
Simplify the numerator.
Multiply a-1 by a6 by adding the exponents.
Move a6.
(3(a6a-1)b4b45)-2
Use the power rule aman=am+n to combine exponents.
(3a6-1b4b45)-2
Subtract 1 from 6.
(3a5b4b45)-2
(3a5b4b45)-2
Multiply b4 by b4 by adding the exponents.
Move b4.
(3a5(b4b4)5)-2
Use the power rule aman=am+n to combine exponents.
(3a5b4+45)-2
(3a5b85)-2
(3a5b85)-2
(3a5b85)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(53a5b8)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 53a5b8.
52(3a5b8)2
Apply the product rule to 3a5b8.
52(3a5)2(b8)2
Apply the product rule to 3a5.
5232(a5)2(b8)2
5232(a5)2(b8)2
Raise 5 to the power of 2.
2532(a5)2(b8)2
Simplify the denominator.
Raise 3 to the power of 2.
259(a5)2(b8)2
Multiply the exponents in (a5)2.
Apply the power rule and multiply exponents, (am)n=amn.
259a5⋅2(b8)2
Multiply 5 by 2.
259a10(b8)2
259a10(b8)2
Multiply the exponents in (b8)2.
Apply the power rule and multiply exponents, (am)n=amn.
259a10b8⋅2
Multiply 8 by 2.
259a10b16
259a10b16
259a10b16
Simplify ((3a^-1b^4)/(5b^-4a^-6))^-2

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