Simplify (4a^3bc^-6)^-3

Math
(4a3bc-6)-3
Rewrite the expression using the negative exponent rule b-n=1bn.
(4a3b1c6)-3
Multiply 4a3b1c6.
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Combine 4 and 1c6.
(a3b4c6)-3
Combine a3 and 4c6.
(ba3⋅4c6)-3
Combine b and a3⋅4c6.
(b(a3⋅4)c6)-3
(b(a3⋅4)c6)-3
Move 4 to the left of ba3.
(4⋅(ba3)c6)-3
Change the sign of the exponent by rewriting the base as its reciprocal.
(c64ba3)3
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to c64ba3.
(c6)3(4ba3)3
Apply the product rule to 4ba3.
(c6)3(4b)3(a3)3
Apply the product rule to 4b.
(c6)343b3(a3)3
(c6)343b3(a3)3
Multiply the exponents in (c6)3.
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Apply the power rule and multiply exponents, (am)n=amn.
c6⋅343b3(a3)3
Multiply 6 by 3.
c1843b3(a3)3
c1843b3(a3)3
Simplify the denominator.
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Raise 4 to the power of 3.
c1864b3(a3)3
Multiply the exponents in (a3)3.
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Apply the power rule and multiply exponents, (am)n=amn.
c1864b3a3⋅3
Multiply 3 by 3.
c1864b3a9
c1864b3a9
c1864b3a9
Simplify (4a^3bc^-6)^-3

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