Simplify (2m^-3)(-mn)^3

Math
(2m-3)(-mn)3
Rewrite the expression using the negative exponent rule b-n=1bn.
21m3(-mn)3
Combine 2 and 1m3.
2m3(-mn)3
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -mn.
2m3((-m)3n3)
Apply the product rule to -m.
2m3((-1)3m3n3)
2m3((-1)3m3n3)
Simplify the expression.
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Rewrite using the commutative property of multiplication.
(-1)32m3(m3n3)
Raise -1 to the power of 3.
-2m3(m3n3)
-2m3(m3n3)
Cancel the common factor of m3.
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Move the leading negative in -2m3 into the numerator.
-2m3(m3n3)
Factor m3 out of m3n3.
-2m3(m3(n3))
Cancel the common factor.
-2m3(m3n3)
Rewrite the expression.
-2n3
-2n3
Simplify (2m^-3)(-mn)^3

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