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

Math
((a)3⋅a54)2÷a7
Rewrite the division as a fraction.
((a)3⋅a54)2a7
Simplify the numerator.
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Apply the product rule to (a)3⋅a54.
((a)3)2⋅a542a7
Multiply the exponents in ((a)3)2.
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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.
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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.
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Factor 2 out of 6.
a2⋅32⋅a542a7
Cancel the common factors.
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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.
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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.
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Factor 2 out of 2.
a3⋅(a2a2(1)4)a7
Cancel the common factors.
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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.
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Rewrite a7 as (a3)2a.
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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.
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Use the power rule aman=am+n to combine exponents.
a3+2aa3a
Add 3 and 2.
a5aa3a
a5aa3a
Reduce the expression by cancelling the common factors.
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Cancel the common factor of a5 and a3.
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Factor a3 out of a5a.
a3(a2a)a3a
Cancel the common factors.
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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.
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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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