Simplify ((3m^2)/(2m^4n^3))^4

Math
(3m22m4n3)4
Cancel the common factor of m2 and m4.
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Factor m2 out of 3m2.
(m2⋅32m4n3)4
Cancel the common factors.
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Factor m2 out of 2m4n3.
(m2⋅3m2(2m2n3))4
Cancel the common factor.
(m2⋅3m2(2m2n3))4
Rewrite the expression.
(32m2n3)4
(32m2n3)4
(32m2n3)4
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to 32m2n3.
34(2m2n3)4
Apply the product rule to 2m2n3.
34(2m2)4(n3)4
Apply the product rule to 2m2.
3424(m2)4(n3)4
3424(m2)4(n3)4
Raise 3 to the power of 4.
8124(m2)4(n3)4
Simplify the denominator.
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Raise 2 to the power of 4.
8116(m2)4(n3)4
Multiply the exponents in (m2)4.
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Apply the power rule and multiply exponents, (am)n=amn.
8116m2⋅4(n3)4
Multiply 2 by 4.
8116m8(n3)4
8116m8(n3)4
Multiply the exponents in (n3)4.
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Apply the power rule and multiply exponents, (am)n=amn.
8116m8n3⋅4
Multiply 3 by 4.
8116m8n12
8116m8n12
8116m8n12
Simplify ((3m^2)/(2m^4n^3))^4

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