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.

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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)

Simplify the numerator.

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Raise 2 to the power of 3.

8w3(z3)3(y4)3(w2z-1)

Multiply the exponents in (z3)3.

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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)

Multiply the exponents in (y4)3.

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Apply the power rule and multiply exponents, (am)n=amn.

8w3z9y4⋅3(w2z-1)

Multiply 4 by 3.

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.

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Factor z out of 8w3z9.

z(8w3z8)y12⋅w2z

Cancel the common factor.

z(8w3z8)y12⋅w2z

Rewrite the expression.

8w3z8y12w2

Combine 8w3z8y12 and w2.

8w3z8w2y12

Multiply w3 by w2 by adding the exponents.

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Move w2.

8(w2w3)z8y12

Use the power rule aman=am+n to combine exponents.

8w2+3z8y12

Add 2 and 3.

8w5z8y12

Simplify ((2wy^-4)/(z^-3))^3(w^2z^-1)

Solving MATH problems