Simplify ((3a^7b^7)/(6a^5))^3

Math
(3a7b76a5)3
Cancel the common factor of 3 and 6.
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Factor 3 out of 3a7b7.
(3(a7b7)6a5)3
Cancel the common factors.
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Factor 3 out of 6a5.
(3(a7b7)3(2a5))3
Cancel the common factor.
(3(a7b7)3(2a5))3
Rewrite the expression.
(a7b72a5)3
(a7b72a5)3
(a7b72a5)3
Cancel the common factor of a7 and a5.
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Factor a5 out of a7b7.
(a5(a2b7)2a5)3
Cancel the common factors.
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Factor a5 out of 2a5.
(a5(a2b7)a5⋅2)3
Cancel the common factor.
(a5(a2b7)a5⋅2)3
Rewrite the expression.
(a2b72)3
(a2b72)3
(a2b72)3
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to a2b72.
(a2b7)323
Apply the product rule to a2b7.
(a2)3(b7)323
(a2)3(b7)323
Simplify the numerator.
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Multiply the exponents in (a2)3.
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Apply the power rule and multiply exponents, (am)n=amn.
a2⋅3(b7)323
Multiply 2 by 3.
a6(b7)323
a6(b7)323
Multiply the exponents in (b7)3.
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Apply the power rule and multiply exponents, (am)n=amn.
a6b7⋅323
Multiply 7 by 3.
a6b2123
a6b2123
a6b2123
Raise 2 to the power of 3.
a6b218
Simplify ((3a^7b^7)/(6a^5))^3

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