Simplify ((a^7)/(8b^3*(a^2-b^2)))/(((a-b)*a^-1)/(8b^2*(a+b)))

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a78b3⋅(a2-b2)(a-b)⋅a-18b2⋅(a+b)
Multiply the numerator by the reciprocal of the denominator.
a78b3⋅(a2-b2)⋅8b2⋅(a+b)(a-b)⋅a-1
Combine.
a7(8b2⋅(a+b))8b3⋅(a2-b2)((a-b)⋅a-1)
Move a-1 to the numerator using the negative exponent rule 1b-n=bn.
a7(8b2⋅(a+b))a8b3⋅(a2-b2)(a-b)
Multiply a7 by a by adding the exponents.
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Move a.
a⋅a7(8b2⋅(a+b))8b3⋅(a2-b2)(a-b)
Multiply a by a7.
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Raise a to the power of 1.
a1a7(8b2⋅(a+b))8b3⋅(a2-b2)(a-b)
Use the power rule aman=am+n to combine exponents.
a1+7(8b2⋅(a+b))8b3⋅(a2-b2)(a-b)
a1+7(8b2⋅(a+b))8b3⋅(a2-b2)(a-b)
Add 1 and 7.
a8(8b2⋅(a+b))8b3⋅(a2-b2)(a-b)
a8(8b2⋅(a+b))8b3⋅(a2-b2)(a-b)
Reduce the expression by cancelling the common factors.
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Cancel the common factor of 8.
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Cancel the common factor.
a8(8b2⋅(a+b))8b3⋅(a2-b2)(a-b)
Rewrite the expression.
a8(b2⋅(a+b))(b3⋅(a2-b2))(a-b)
a8(b2⋅(a+b))(b3⋅(a2-b2))(a-b)
Cancel the common factor of b2 and b3.
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Factor b2 out of a8(b2⋅(a+b)).
b2(a8(a+b))(b3⋅(a2-b2))(a-b)
Cancel the common factors.
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Factor b2 out of (b3⋅(a2-b2))(a-b).
b2(a8(a+b))b2((b⋅(a2-b2))(a-b))
Cancel the common factor.
b2(a8(a+b))b2((b⋅(a2-b2))(a-b))
Rewrite the expression.
a8(a+b)(b⋅(a2-b2))(a-b)
a8(a+b)(b⋅(a2-b2))(a-b)
a8(a+b)(b⋅(a2-b2))(a-b)
a8(a+b)(b⋅(a2-b2))(a-b)
Simplify the denominator.
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Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=b.
a8(a+b)b⋅(a+b)(a-b)(a-b)
Combine exponents.
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Raise a-b to the power of 1.
a8(a+b)b⋅(a+b)((a-b)1(a-b))
Raise a-b to the power of 1.
a8(a+b)b⋅(a+b)((a-b)1(a-b)1)
Use the power rule aman=am+n to combine exponents.
a8(a+b)b⋅(a+b)(a-b)1+1
Add 1 and 1.
a8(a+b)b⋅(a+b)(a-b)2
a8(a+b)b⋅(a+b)(a-b)2
a8(a+b)b⋅(a+b)(a-b)2
Cancel the common factor of a+b.
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Cancel the common factor.
a8(a+b)b⋅(a+b)(a-b)2
Rewrite the expression.
a8b(a-b)2
a8b(a-b)2
Simplify ((a^7)/(8b^3*(a^2-b^2)))/(((a-b)*a^-1)/(8b^2*(a+b)))

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