Simplify (7ab)(-a^4b^3)^2(2a^5b^6)^-1

Math
(7ab)(-a4b3)2(2a5b6)-1
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -a4b3.
7ab((-a4)2(b3)2)(2a5b6)-1
Apply the product rule to -a4.
7ab((-1)2(a4)2(b3)2)(2a5b6)-1
7ab((-1)2(a4)2(b3)2)(2a5b6)-1
Raise -1 to the power of 2.
7ab(1(a4)2(b3)2)(2a5b6)-1
Multiply (a4)2 by 1.
7ab((a4)2(b3)2)(2a5b6)-1
Multiply the exponents in (a4)2.
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Apply the power rule and multiply exponents, (am)n=amn.
7ab(a4⋅2(b3)2)(2a5b6)-1
Multiply 4 by 2.
7ab(a8(b3)2)(2a5b6)-1
7ab(a8(b3)2)(2a5b6)-1
Multiply a by a8 by adding the exponents.
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Move a8.
7(a8a)b(b3)2(2a5b6)-1
Multiply a8 by a.
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Raise a to the power of 1.
7(a8a1)b(b3)2(2a5b6)-1
Use the power rule aman=am+n to combine exponents.
7a8+1b(b3)2(2a5b6)-1
7a8+1b(b3)2(2a5b6)-1
Add 8 and 1.
7a9b(b3)2(2a5b6)-1
7a9b(b3)2(2a5b6)-1
Multiply the exponents in (b3)2.
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Apply the power rule and multiply exponents, (am)n=amn.
7a9b⋅b3⋅2(2a5b6)-1
Multiply 3 by 2.
7a9b⋅b6(2a5b6)-1
7a9b⋅b6(2a5b6)-1
Multiply b by b6 by adding the exponents.
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Move b6.
7a9(b6b)(2a5b6)-1
Multiply b6 by b.
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Raise b to the power of 1.
7a9(b6b1)(2a5b6)-1
Use the power rule aman=am+n to combine exponents.
7a9b6+1(2a5b6)-1
7a9b6+1(2a5b6)-1
Add 6 and 1.
7a9b7(2a5b6)-1
7a9b7(2a5b6)-1
Rewrite the expression using the negative exponent rule b-n=1bn.
7a9b712a5b6
Cancel the common factor of a5b6.
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Factor a5b6 out of 7a9b7.
a5b6(7a4b)12a5b6
Factor a5b6 out of 2a5b6.
a5b6(7a4b)1a5b6(2)
Cancel the common factor.
a5b6(7a4b)1a5b6⋅2
Rewrite the expression.
7a4b12
7a4b12
Combine 7 and 12.
a4b72
Combine a4 and 72.
ba4⋅72
Combine b and a4⋅72.
b(a4⋅7)2
Move 7 to the left of ba4.
7ba42
Simplify (7ab)(-a^4b^3)^2(2a^5b^6)^-1

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