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

(3ab)3(4a3b)2
Use the power rule (ab)n=anbn to distribute the exponent.
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.
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.
Move b2.
27a3(b2b3)(42(a3)2)
Use the power rule aman=am+n to combine exponents.
27a3b2+3(42(a3)2)
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.
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.
Move a6.
27(a6a3)b5⋅16
Use the power rule aman=am+n to combine exponents.
27a6+3b5⋅16