# Simplify (uv^3)(-2u^3vw^2)^-3

(uv3)(-2u3vw2)-3
Rewrite the expression using the negative exponent rule b-n=1bn.
uv31(-2u3vw2)3
Simplify the denominator.
Apply the product rule to -2u3vw2.
uv31(-2u3v)3(w2)3
Apply the product rule to -2u3v.
uv31(-2u3)3v3(w2)3
Apply the product rule to -2u3.
uv31(-2)3(u3)3v3(w2)3
Raise -2 to the power of 3.
uv31-8(u3)3v3(w2)3
Multiply the exponents in (u3)3.
Apply the power rule and multiply exponents, (am)n=amn.
uv31-8u3⋅3v3(w2)3
Multiply 3 by 3.
uv31-8u9v3(w2)3
uv31-8u9v3(w2)3
Multiply the exponents in (w2)3.
Apply the power rule and multiply exponents, (am)n=amn.
uv31-8u9v3w2⋅3
Multiply 2 by 3.
uv31-8u9v3w6
uv31-8u9v3w6
uv31-8u9v3w6
Reduce the expression by cancelling the common factors.
Cancel the common factor of uv3.
Factor uv3 out of -8u9v3w6.
uv31uv3(-8u8w6)
Cancel the common factor.
uv31uv3(-8u8w6)
Rewrite the expression.
1-8u8w6
1-8u8w6
Move the negative in front of the fraction.
-18u8w6
-18u8w6
Simplify (uv^3)(-2u^3vw^2)^-3

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