# Simplify (((m*3)/4*(n*1)/4)^2)/(((m*1)/4*n^(-1/2))^3) (m⋅34⋅n⋅14)2(m⋅14⋅n-12)3
Simplify.
Multiply n by 1.
(m⋅34⋅n4)2(m⋅14⋅n-12)3
Multiply m by 1.
(m⋅34⋅n4)2(m4⋅n-12)3
(m⋅34⋅n4)2(m4⋅n-12)3
Simplify the numerator.
Apply the product rule to m⋅34⋅n4.
(m⋅34)2⋅(n4)2(m4⋅n-12)3
Apply the product rule to m⋅34.
(m⋅3)242⋅(n4)2(m4⋅n-12)3
Apply the product rule to m⋅3.
m2⋅3242⋅(n4)2(m4⋅n-12)3
Raise 3 to the power of 2.
m2⋅942⋅(n4)2(m4⋅n-12)3
Raise 4 to the power of 2.
m2⋅916⋅(n4)2(m4⋅n-12)3
Move 9 to the left of m2.
9⋅m216⋅(n4)2(m4⋅n-12)3
Apply the product rule to n4.
9m216⋅n242(m4⋅n-12)3
Raise 4 to the power of 2.
9m216⋅n216(m4⋅n-12)3
9m216⋅n216(m4⋅n-12)3
Simplify the denominator.
Apply the product rule to m4⋅n-12.
9m216⋅n216(m4)3⋅(n-12)3
Apply the product rule to m4.
9m216⋅n216m343⋅(n-12)3
Raise 4 to the power of 3.
9m216⋅n216m364⋅(n-12)3
Multiply the exponents in (n-12)3.
Apply the power rule and multiply exponents, (am)n=amn.
9m216⋅n216m364⋅n-12⋅3
Multiply -12⋅3.
Multiply 3 by -1.
9m216⋅n216m364⋅n-3(12)
Combine -3 and 12.
9m216⋅n216m364⋅n-32
9m216⋅n216m364⋅n-32
Move the negative in front of the fraction.
9m216⋅n216m364⋅n-32
9m216⋅n216m364⋅n-32
Rewrite the expression using the negative exponent rule b-n=1bn.
9m216⋅n216m364⋅1n32
9m216⋅n216m364⋅1n32
Multiply 9m216 and n216.
9m2n216⋅16m364⋅1n32
Multiply m364 and 1n32.
9m2n216⋅16m364n32
Multiply 16 by 16.
9m2n2256m364n32
Multiply the numerator by the reciprocal of the denominator.
9m2n2256⋅64n32m3
Cancel the common factor of m2.
Factor m2 out of 9m2n2.
m2(9n2)256⋅64n32m3
Factor m2 out of m3.
m2(9n2)256⋅64n32m2m
Cancel the common factor.
m2(9n2)256⋅64n32m2m
Rewrite the expression.
9n2256⋅64n32m
9n2256⋅64n32m
Cancel the common factor of 64.
Factor 64 out of 256.
9n264(4)⋅64n32m
Factor 64 out of 64n32.
9n264(4)⋅64(n32)m
Cancel the common factor.
9n264⋅4⋅64n32m
Rewrite the expression.
9n24⋅n32m
9n24⋅n32m
Multiply 9n24 and n32m.
9n2n324m
Multiply n2 by n32 by adding the exponents.
Move n32.
9(n32n2)4m
Use the power rule aman=am+n to combine exponents.
9n32+24m
To write 2 as a fraction with a common denominator, multiply by 22.
9n32+2⋅224m
Combine 2 and 22.
9n32+2⋅224m
Combine the numerators over the common denominator.
9n3+2⋅224m
Simplify the numerator.
Multiply 2 by 2.
9n3+424m
Add 3 and 4.
9n724m
9n724m
9n724m
Simplify (((m*3)/4*(n*1)/4)^2)/(((m*1)/4*n^(-1/2))^3)

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