Simplify (3ab)^3(4a^3b)^2

Math
(3ab)3(4a3b)2
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to 3ab.
(3a)3b3(4a3b)2
Apply the product rule to 3a.
33a3b3(4a3b)2
33a3b3(4a3b)2
Raise 3 to the power of 3.
27a3b3(4a3b)2
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to 4a3b.
27a3b3((4a3)2b2)
Apply the product rule to 4a3.
27a3b3(42(a3)2b2)
27a3b3(42(a3)2b2)
Multiply b3 by b2 by adding the exponents.
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Move b2.
27a3(b2b3)(42(a3)2)
Use the power rule aman=am+n to combine exponents.
27a3b2+3(42(a3)2)
Add 2 and 3.
27a3b5(42(a3)2)
27a3b5(42(a3)2)
Raise 4 to the power of 2.
27a3b5(16(a3)2)
Multiply the exponents in (a3)2.
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Apply the power rule and multiply exponents, (am)n=amn.
27a3b5(16a3⋅2)
Multiply 3 by 2.
27a3b5(16a6)
27a3b5(16a6)
Multiply a3 by a6 by adding the exponents.
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Move a6.
27(a6a3)b5⋅16
Use the power rule aman=am+n to combine exponents.
27a6+3b5⋅16
Add 6 and 3.
27a9b5⋅16
27a9b5⋅16
Multiply 16 by 27.
432a9b5
Simplify (3ab)^3(4a^3b)^2

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