Simplify (uv)/((2u^4v^-2)^2*(u^2v^-1))

Math
uv(2u4v-2)2⋅(u2v-1)
Move v-1 to the numerator using the negative exponent rule 1b-n=bn.
uv⋅v(2u4v-2)2⋅u2
Multiply v by v by adding the exponents.
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Move v.
u(v⋅v)(2u4v-2)2⋅u2
Multiply v by v.
uv2(2u4v-2)2⋅u2
uv2(2u4v-2)2⋅u2
Cancel the common factor of u and u2.
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Factor u out of uv2.
u(v2)(2u4v-2)2⋅u2
Cancel the common factors.
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Factor u out of (2u4v-2)2⋅u2.
u(v2)u((2u4v-2)2⋅u)
Cancel the common factor.
uv2u((2u4v-2)2⋅u)
Rewrite the expression.
v2(2u4v-2)2⋅u
v2(2u4v-2)2⋅u
v2(2u4v-2)2⋅u
Simplify the denominator.
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Apply the product rule to 2u4v-2.
v2(2u4)2(v-2)2u
Apply the product rule to 2u4.
v222(u4)2(v-2)2u
Raise 2 to the power of 2.
v24(u4)2(v-2)2u
Multiply the exponents in (u4)2.
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Apply the power rule and multiply exponents, (am)n=amn.
v24u4⋅2(v-2)2u
Multiply 4 by 2.
v24u8(v-2)2u
v24u8(v-2)2u
Multiply the exponents in (v-2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
v24u8v-2⋅2u
Multiply -2 by 2.
v24u8v-4u
v24u8v-4u
Rewrite the expression using the negative exponent rule b-n=1bn.
v24u81v4u
v24u81v4u
Simplify the denominator.
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Combine 4 and 1v4.
v2u84v4u
Combine u8 and 4v4.
v2u8⋅4v4u
Combine u8⋅4v4 and u.
v2u8⋅4uv4
v2u8⋅4uv4
Simplify the numerator.
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Raise u to the power of 1.
v24(u8u1)v4
Use the power rule aman=am+n to combine exponents.
v24u8+1v4
Add 8 and 1.
v24u9v4
v24u9v4
Multiply the numerator by the reciprocal of the denominator.
v2v44u9
Multiply v2v44u9.
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Combine v2 and v44u9.
v2v44u9
Multiply v2 by v4 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
v2+44u9
Add 2 and 4.
v64u9
v64u9
v64u9
Simplify (uv)/((2u^4v^-2)^2*(u^2v^-1))

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