Simplify ((w^2z^4)^3)/((-wz^5)^2(w^4z^2))

Math
(w2z4)3(-wz5)2(w4z2)
Simplify the numerator.
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Apply the product rule to w2z4.
(w2)3(z4)3(-wz5)2w4z2
Multiply the exponents in (w2)3.
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Apply the power rule and multiply exponents, (am)n=amn.
w2⋅3(z4)3(-wz5)2w4z2
Multiply 2 by 3.
w6(z4)3(-wz5)2w4z2
w6(z4)3(-wz5)2w4z2
Multiply the exponents in (z4)3.
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Apply the power rule and multiply exponents, (am)n=amn.
w6z4⋅3(-wz5)2w4z2
Multiply 4 by 3.
w6z12(-wz5)2w4z2
w6z12(-wz5)2w4z2
w6z12(-wz5)2w4z2
Simplify the denominator.
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Apply the product rule to -wz5.
w6z12(-w)2(z5)2w4z2
Combine exponents.
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Factor -1 out of -w.
w6z12(-(w))2(z5)2w4z2
Rewrite -(w) as -1(w).
w6z12(-1(w))2(z5)2w4z2
Apply the product rule to -1(w).
w6z12(-1)2w2(z5)2w4z2
Raise -1 to the power of 2.
w6z121w2(z5)2w4z2
Multiply w2 by 1.
w6z12w2(z5)2w4z2
Multiply w2 by w4 by adding the exponents.
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Move w4.
w6z12w4w2(z5)2z2
Use the power rule aman=am+n to combine exponents.
w6z12w4+2(z5)2z2
Add 4 and 2.
w6z12w6(z5)2z2
w6z12w6(z5)2z2
w6z12w6(z5)2z2
Multiply the exponents in (z5)2.
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Apply the power rule and multiply exponents, (am)n=amn.
w6z12w6z5⋅2z2
Multiply 5 by 2.
w6z12w6z10z2
w6z12w6z10z2
w6z12w6z10z2
Multiply z10 by z2 by adding the exponents.
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Move z2.
w6z12w6(z2z10)
Use the power rule aman=am+n to combine exponents.
w6z12w6z2+10
Add 2 and 10.
w6z12w6z12
w6z12w6z12
Cancel the common factor of w6.
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Cancel the common factor.
w6z12w6z12
Rewrite the expression.
z12z12
z12z12
Cancel the common factor of z12.
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Cancel the common factor.
z12z12
Divide 1 by 1.
1
1
Simplify ((w^2z^4)^3)/((-wz^5)^2(w^4z^2))

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