# Simplify ((2wy^-4)/(z^-3))^3(w^2z^-1) (2wy-4z-3)3(w2z-1)
Move y-4 to the denominator using the negative exponent rule b-n=1bn.
(2wz-3y4)3(w2z-1)
Move z-3 to the numerator using the negative exponent rule 1b-n=bn.
(2wz3y4)3(w2z-1)
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 2wz3y4.
(2wz3)3(y4)3(w2z-1)
Apply the product rule to 2wz3.
(2w)3(z3)3(y4)3(w2z-1)
Apply the product rule to 2w.
23w3(z3)3(y4)3(w2z-1)
23w3(z3)3(y4)3(w2z-1)
Simplify the numerator.
Raise 2 to the power of 3.
8w3(z3)3(y4)3(w2z-1)
Multiply the exponents in (z3)3.
Apply the power rule and multiply exponents, (am)n=amn.
8w3z3⋅3(y4)3(w2z-1)
Multiply 3 by 3.
8w3z9(y4)3(w2z-1)
8w3z9(y4)3(w2z-1)
8w3z9(y4)3(w2z-1)
Multiply the exponents in (y4)3.
Apply the power rule and multiply exponents, (am)n=amn.
8w3z9y4⋅3(w2z-1)
Multiply 4 by 3.
8w3z9y12(w2z-1)
8w3z9y12(w2z-1)
Rewrite the expression using the negative exponent rule b-n=1bn.
8w3z9y12(w21z)
Combine w2 and 1z.
8w3z9y12⋅w2z
Cancel the common factor of z.
Factor z out of 8w3z9.
z(8w3z8)y12⋅w2z
Cancel the common factor.
z(8w3z8)y12⋅w2z
Rewrite the expression.
8w3z8y12w2
8w3z8y12w2
Combine 8w3z8y12 and w2.
8w3z8w2y12
Multiply w3 by w2 by adding the exponents.
Move w2.
8(w2w3)z8y12
Use the power rule aman=am+n to combine exponents.
8w2+3z8y12