Simplify (a^8b*(a^6b^2))/((a^2b^5)^2)

Math
a8b⋅(a6b2)(a2b5)2
Multiply a8 by a6 by adding the exponents.
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Move a6.
a6a8b⋅b2(a2b5)2
Use the power rule aman=am+n to combine exponents.
a6+8b⋅b2(a2b5)2
Add 6 and 8.
a14b⋅b2(a2b5)2
a14b⋅b2(a2b5)2
Multiply b by b2 by adding the exponents.
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Move b2.
a14(b2b)(a2b5)2
Multiply b2 by b.
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Raise b to the power of 1.
a14(b2b1)(a2b5)2
Use the power rule aman=am+n to combine exponents.
a14b2+1(a2b5)2
a14b2+1(a2b5)2
Add 2 and 1.
a14b3(a2b5)2
a14b3(a2b5)2
Simplify the denominator.
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Apply the product rule to a2b5.
a14b3(a2)2(b5)2
Multiply the exponents in (a2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
a14b3a2⋅2(b5)2
Multiply 2 by 2.
a14b3a4(b5)2
a14b3a4(b5)2
Multiply the exponents in (b5)2.
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Apply the power rule and multiply exponents, (am)n=amn.
a14b3a4b5⋅2
Multiply 5 by 2.
a14b3a4b10
a14b3a4b10
a14b3a4b10
Reduce the expression by cancelling the common factors.
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Cancel the common factor of a14 and a4.
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Factor a4 out of a14b3.
a4(a10b3)a4b10
Cancel the common factors.
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Factor a4 out of a4b10.
a4(a10b3)a4(b10)
Cancel the common factor.
a4(a10b3)a4b10
Rewrite the expression.
a10b3b10
a10b3b10
a10b3b10
Cancel the common factor of b3 and b10.
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Factor b3 out of a10b3.
b3a10b10
Cancel the common factors.
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Factor b3 out of b10.
b3a10b3b7
Cancel the common factor.
b3a10b3b7
Rewrite the expression.
a10b7
a10b7
a10b7
a10b7
Simplify (a^8b*(a^6b^2))/((a^2b^5)^2)

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