# Simplify ((( square root of a)^3* fourth root of a^5)^2)÷( square root of a^7)

((a)3⋅a54)2÷a7
Rewrite the division as a fraction.
((a)3⋅a54)2a7
Simplify the numerator.
Apply the product rule to (a)3⋅a54.
((a)3)2⋅a542a7
Multiply the exponents in ((a)3)2.
Apply the power rule and multiply exponents, (am)n=amn.
a3⋅2⋅a542a7
Multiply 3 by 2.
a6⋅a542a7
a6⋅a542a7
Rewrite a6 as a3.
Use axn=axn to rewrite a as a12.
(a12)6⋅a542a7
Apply the power rule and multiply exponents, (am)n=amn.
a12⋅6⋅a542a7
Combine 12 and 6.
a62⋅a542a7
Cancel the common factor of 6 and 2.
Factor 2 out of 6.
a2⋅32⋅a542a7
Cancel the common factors.
Factor 2 out of 2.
a2⋅32(1)⋅a542a7
Cancel the common factor.
a2⋅32⋅1⋅a542a7
Rewrite the expression.
a31⋅a542a7
Divide 3 by 1.
a3⋅a542a7
a3⋅a542a7
a3⋅a542a7
a3⋅a542a7
Factor out a4.
a3⋅a4a42a7
Pull terms out from under the radical.
a3⋅(aa4)2a7
Apply the product rule to aa4.
a3⋅(a2a42)a7
Rewrite a42 as a.
Use axn=axn to rewrite a4 as a14.
a3⋅(a2(a14)2)a7
Apply the power rule and multiply exponents, (am)n=amn.
a3⋅(a2a14⋅2)a7
Combine 14 and 2.
a3⋅(a2a24)a7
Cancel the common factor of 2 and 4.
Factor 2 out of 2.
a3⋅(a2a2(1)4)a7
Cancel the common factors.
Factor 2 out of 4.
a3⋅(a2a2⋅12⋅2)a7
Cancel the common factor.
a3⋅(a2a2⋅12⋅2)a7
Rewrite the expression.
a3⋅(a2a12)a7
a3⋅(a2a12)a7
a3⋅(a2a12)a7
Rewrite a12 as a.
a3⋅(a2a)a7
a3⋅(a2a)a7
a3⋅(a2a)a7
Simplify the denominator.
Rewrite a7 as (a3)2a.
Factor out a6.
a3⋅(a2a)a6a
Rewrite a6 as (a3)2.
a3⋅(a2a)(a3)2a
a3⋅(a2a)(a3)2a
Pull terms out from under the radical.
a3⋅(a2a)a3a
a3⋅(a2a)a3a
Simplify the numerator.
Use the power rule aman=am+n to combine exponents.
a3+2aa3a
a5aa3a
a5aa3a
Reduce the expression by cancelling the common factors.
Cancel the common factor of a5 and a3.
Factor a3 out of a5a.
a3(a2a)a3a
Cancel the common factors.
Factor a3 out of a3a.
a3(a2a)a3(a)
Cancel the common factor.
a3(a2a)a3a
Rewrite the expression.
a2aa
a2aa
a2aa
Cancel the common factor of a.
Cancel the common factor.
a2aa
Divide a2 by 1.
a2
a2
a2
Simplify ((( square root of a)^3* fourth root of a^5)^2)÷( square root of a^7)

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