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

(14a4b6)2(a6c3)7
Use the power rule (ab)n=anbn to distribute the exponent.
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.
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.
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.
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.
Move a42.
196(a42a8)b12(c3)7
Use the power rule aman=am+n to combine exponents.
196a42+8b12(c3)7
196a50b12(c3)7
196a50b12(c3)7
Multiply the exponents in (c3)7.
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