Simplify ((m^7n^-5)^3*(m^8n^-7))^-1

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((m7n-5)3⋅(m8n-7))-1
Rewrite the expression using the negative exponent rule b-n=1bn.
((m71n5)3⋅(m8n-7))-1
Combine m7 and 1n5.
((m7n5)3⋅(m8n-7))-1
Apply basic rules of exponents.
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Apply the product rule to m7n5.
((m7)3(n5)3⋅(m8n-7))-1
Multiply the exponents in (m7)3.
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Apply the power rule and multiply exponents, (am)n=amn.
(m7⋅3(n5)3⋅(m8n-7))-1
Multiply 7 by 3.
(m21(n5)3⋅(m8n-7))-1
(m21(n5)3⋅(m8n-7))-1
Multiply the exponents in (n5)3.
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Apply the power rule and multiply exponents, (am)n=amn.
(m21n5⋅3⋅(m8n-7))-1
Multiply 5 by 3.
(m21n15⋅(m8n-7))-1
(m21n15⋅(m8n-7))-1
(m21n15⋅(m8n-7))-1
Cancel the common factor of n-7.
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Factor n-7 out of n15.
(m21n-7n22⋅(m8n-7))-1
Factor n-7 out of m8n-7.
(m21n-7n22⋅(n-7m8))-1
Cancel the common factor.
(m21n-7n22⋅(n-7m8))-1
Rewrite the expression.
(m21n22⋅m8)-1
(m21n22⋅m8)-1
Combine m21n22 and m8.
(m21m8n22)-1
Multiply m21 by m8 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(m21+8n22)-1
Add 21 and 8.
(m29n22)-1
(m29n22)-1
Change the sign of the exponent by rewriting the base as its reciprocal.
n22m29
Simplify ((m^7n^-5)^3*(m^8n^-7))^-1

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