# Multiply (5xy^4)^3*(x^2y)

(5xy4)3⋅(x2y)
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 5xy4.
(5x)3(y4)3⋅(x2y)
Apply the product rule to 5x.
53×3(y4)3⋅(x2y)
53×3(y4)3⋅(x2y)
Multiply x3 by x2 by adding the exponents.
Move x2.
53(x2x3)(y4)3⋅y
Use the power rule aman=am+n to combine exponents.
53×2+3(y4)3⋅y
53×5(y4)3⋅y
53×5(y4)3⋅y
Raise 5 to the power of 3.
125×5(y4)3⋅y
Multiply the exponents in (y4)3.
Apply the power rule and multiply exponents, (am)n=amn.
125x5y4⋅3⋅y
Multiply 4 by 3.
125x5y12⋅y
125x5y12⋅y
Multiply y12 by y by adding the exponents.
Move y.
125×5(y⋅y12)
Multiply y by y12.
Raise y to the power of 1.
125×5(y1y12)
Use the power rule aman=am+n to combine exponents.
125x5y1+12
125x5y1+12