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

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.
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.
Factor u out of uv2.
u(v2)(2u4v-2)2⋅u2
Cancel the common factors.
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.
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.
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.
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.
Combine 4 and 1v4.
v2u84v4u
Combine u8 and 4v4.
v2u8⋅4v4u
Combine u8⋅4v4 and u.
v2u8⋅4uv4
v2u8⋅4uv4
Simplify the numerator.
Raise u to the power of 1.
v24(u8u1)v4
Use the power rule aman=am+n to combine exponents.
v24u8+1v4
v24u9v4
v24u9v4
Multiply the numerator by the reciprocal of the denominator.
v2v44u9
Multiply v2v44u9.
Combine v2 and v44u9.
v2v44u9
Multiply v2 by v4 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
v2+44u9