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

a8b⋅(a6b2)(a2b5)2
Multiply a8 by a6 by adding the exponents.
Move a6.
a6a8b⋅b2(a2b5)2
Use the power rule aman=am+n to combine exponents.
a6+8b⋅b2(a2b5)2
a14b⋅b2(a2b5)2
a14b⋅b2(a2b5)2
Multiply b by b2 by adding the exponents.
Move b2.
a14(b2b)(a2b5)2
Multiply b2 by b.
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
a14b3(a2b5)2
a14b3(a2b5)2
Simplify the denominator.
Apply the product rule to a2b5.
a14b3(a2)2(b5)2
Multiply the exponents in (a2)2.
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.
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.
Cancel the common factor of a14 and a4.
Factor a4 out of a14b3.
a4(a10b3)a4b10
Cancel the common factors.
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.
Factor b3 out of a10b3.
b3a10b10
Cancel the common factors.
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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