Simplify (14a^4b^6)^2(a^6c^3)^7

Math
(14a4b6)2(a6c3)7
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to 14a4b6.
(14a4)2(b6)2(a6c3)7
Apply the product rule to 14a4.
142(a4)2(b6)2(a6c3)7
142(a4)2(b6)2(a6c3)7
Raise 14 to the power of 2.
196(a4)2(b6)2(a6c3)7
Multiply the exponents in (a4)2.
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Apply the power rule and multiply exponents, (am)n=amn.
196a4⋅2(b6)2(a6c3)7
Multiply 4 by 2.
196a8(b6)2(a6c3)7
196a8(b6)2(a6c3)7
Multiply the exponents in (b6)2.
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Apply the power rule and multiply exponents, (am)n=amn.
196a8b6⋅2(a6c3)7
Multiply 6 by 2.
196a8b12(a6c3)7
196a8b12(a6c3)7
Apply the product rule to a6c3.
196a8b12((a6)7(c3)7)
Multiply the exponents in (a6)7.
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Apply the power rule and multiply exponents, (am)n=amn.
196a8b12(a6⋅7(c3)7)
Multiply 6 by 7.
196a8b12(a42(c3)7)
196a8b12(a42(c3)7)
Multiply a8 by a42 by adding the exponents.
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Move a42.
196(a42a8)b12(c3)7
Use the power rule aman=am+n to combine exponents.
196a42+8b12(c3)7
Add 42 and 8.
196a50b12(c3)7
196a50b12(c3)7
Multiply the exponents in (c3)7.
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Apply the power rule and multiply exponents, (am)n=amn.
196a50b12c3⋅7
Multiply 3 by 7.
196a50b12c21
196a50b12c21
Simplify (14a^4b^6)^2(a^6c^3)^7

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