Simplify ( square root of a+1/( square root of a))^7

Math
(a+1a)7
Simplify each term.
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Multiply 1a by aa.
(a+1a⋅aa)7
Combine and simplify the denominator.
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Multiply 1a and aa.
(a+aaa)7
Raise a to the power of 1.
(a+aa1a)7
Raise a to the power of 1.
(a+aa1a1)7
Use the power rule aman=am+n to combine exponents.
(a+aa1+1)7
Add 1 and 1.
(a+aa2)7
Rewrite a2 as a.
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Use axn=axn to rewrite a as a12.
(a+a(a12)2)7
Apply the power rule and multiply exponents, (am)n=amn.
(a+aa12⋅2)7
Combine 12 and 2.
(a+aa22)7
Cancel the common factor of 2.
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Cancel the common factor.
(a+aa22)7
Divide 1 by 1.
(a+aa1)7
(a+aa1)7
Simplify.
(a+aa)7
(a+aa)7
(a+aa)7
(a+aa)7
Use the Binomial Theorem.
a7+7a6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Simplify each term.
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Rewrite a7 as (a7)12.
a7+7a6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a7 as (a3)2a.
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Factor out a6.
a6a+7a6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a6 as (a3)2.
(a3)2a+7a6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
(a3)2a+7a6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Pull terms out from under the radical.
a3a+7a6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a6 as a3.
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Use axn=axn to rewrite a as a12.
a3a+7(a12)6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Apply the power rule and multiply exponents, (am)n=amn.
a3a+7a12⋅6aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Combine 12 and 6.
a3a+7a62aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of 6 and 2.
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Factor 2 out of 6.
a3a+7a2⋅32aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factors.
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Factor 2 out of 2.
a3a+7a2⋅32(1)aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2⋅32⋅1aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a31aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Divide 3 by 1.
a3a+7a3aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a3aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a3aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a3aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of a.
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Factor a out of 7a3.
a3a+a(7a2)aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor.
a3a+a(7a2)aa+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a5 as (a5)12.
a3a+7a2a+21a5(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a5 as (a2)2a.
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Factor out a4.
a3a+7a2a+21a4a(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a4 as (a2)2.
a3a+7a2a+21(a2)2a(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21(a2)2a(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Pull terms out from under the radical.
a3a+7a2a+21(a2a)(aa)2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Apply the product rule to aa.
a3a+7a2a+21a2aa2a2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of a2.
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Factor a2 out of 21a2a.
a3a+7a2a+a2(21a)a2a2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2a+a2(21a)a2a2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa2+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Multiply a by a2 by adding the exponents.
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Move a2.
a3a+7a2a+21(a2a)+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Multiply a2 by a.
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Raise a to the power of 1.
a3a+7a2a+21(a2a1)+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Use the power rule aman=am+n to combine exponents.
a3a+7a2a+21a2+1+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21a2+1+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Add 2 and 1.
a3a+7a2a+21a3+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21a3+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a3 as (a3)12.
a3a+7a2a+21a3+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Factor out a2.
a3a+7a2a+21a2a+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Pull terms out from under the radical.
a3a+7a2a+21(aa)+35a4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a4 as a2.
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Use axn=axn to rewrite a as a12.
a3a+7a2a+21aa+35(a12)4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Apply the power rule and multiply exponents, (am)n=amn.
a3a+7a2a+21aa+35a12⋅4(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Combine 12 and 4.
a3a+7a2a+21aa+35a42(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of 4 and 2.
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Factor 2 out of 4.
a3a+7a2a+21aa+35a2⋅22(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factors.
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Factor 2 out of 2.
a3a+7a2a+21aa+35a2⋅22(1)(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+35a2⋅22⋅1(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a21(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Divide 2 by 1.
a3a+7a2a+21aa+35a2(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a2(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a2(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a2(aa)3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Apply the product rule to aa.
a3a+7a2a+21aa+35a2a3a3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of a2.
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Factor a2 out of 35a2.
a3a+7a2a+21aa+a2⋅35a3a3+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Factor a2 out of a3.
a3a+7a2a+21aa+a2⋅35a3a2a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+a2⋅35a3a2a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a3a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a3a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Combine 35 and a3a.
a3a+7a2a+21aa+35a3a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Simplify the numerator.
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Rewrite a3 as (a3)12.
a3a+7a2a+21aa+35a3a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Factor out a2.
a3a+7a2a+21aa+35a2aa+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Pull terms out from under the radical.
a3a+7a2a+21aa+35aaa+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35aaa+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of a.
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Cancel the common factor.
a3a+7a2a+21aa+35aaa+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Divide 35a by 1.
a3a+7a2a+21aa+35a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a3 as (a3)12.
a3a+7a2a+21aa+35a+35a3(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Factor out a2.
a3a+7a2a+21aa+35a+35a2a(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Pull terms out from under the radical.
a3a+7a2a+21aa+35a+35(aa)(aa)4+21a2(aa)5+7a(aa)6+(aa)7
Apply the product rule to aa.
a3a+7a2a+21aa+35a+35aaa4a4+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of a.
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Factor a out of 35aa.
a3a+7a2a+21aa+35a+a(35a)a4a4+21a2(aa)5+7a(aa)6+(aa)7
Factor a out of a4.
a3a+7a2a+21aa+35a+a(35a)a4a⋅a3+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+35a+a(35a)a4a⋅a3+21a2(aa)5+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a+35aa4a3+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa4a3+21a2(aa)5+7a(aa)6+(aa)7
Combine a4a3 and 35.
a3a+7a2a+21aa+35a+a4⋅35a3a+21a2(aa)5+7a(aa)6+(aa)7
Combine a4⋅35a3 and a.
a3a+7a2a+21aa+35a+a4⋅35aa3+21a2(aa)5+7a(aa)6+(aa)7
Raise a to the power of 1.
a3a+7a2a+21aa+35a+35(a4a1)a3+21a2(aa)5+7a(aa)6+(aa)7
Use the power rule aman=am+n to combine exponents.
a3a+7a2a+21aa+35a+35a4+1a3+21a2(aa)5+7a(aa)6+(aa)7
Add 4 and 1.
a3a+7a2a+21aa+35a+35a5a3+21a2(aa)5+7a(aa)6+(aa)7
Simplify the numerator.
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Rewrite a5 as (a5)12.
a3a+7a2a+21aa+35a+35a5a3+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a5 as (a2)2a.
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Factor out a4.
a3a+7a2a+21aa+35a+35a4aa3+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a4 as (a2)2.
a3a+7a2a+21aa+35a+35(a2)2aa3+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35(a2)2aa3+21a2(aa)5+7a(aa)6+(aa)7
Pull terms out from under the radical.
a3a+7a2a+21aa+35a+35a2aa3+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35a2aa3+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor of a2 and a3.
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Factor a2 out of 35a2a.
a3a+7a2a+21aa+35a+a2(35a)a3+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factors.
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Factor a2 out of a3.
a3a+7a2a+21aa+35a+a2(35a)a2a+21a2(aa)5+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+35a+a2(35a)a2a+21a2(aa)5+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a+35aa+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21a2(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21a2(aa)5+7a(aa)6+(aa)7
Rewrite a2 as a.
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Use axn=axn to rewrite a as a12.
a3a+7a2a+21aa+35a+35aa+21(a12)2(aa)5+7a(aa)6+(aa)7
Apply the power rule and multiply exponents, (am)n=amn.
a3a+7a2a+21aa+35a+35aa+21a12⋅2(aa)5+7a(aa)6+(aa)7
Combine 12 and 2.
a3a+7a2a+21aa+35a+35aa+21a22(aa)5+7a(aa)6+(aa)7
Cancel the common factor of 2.
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Cancel the common factor.
a3a+7a2a+21aa+35a+35aa+21a22(aa)5+7a(aa)6+(aa)7
Divide 1 by 1.
a3a+7a2a+21aa+35a+35aa+21a1(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21a1(aa)5+7a(aa)6+(aa)7
Simplify.
a3a+7a2a+21aa+35a+35aa+21a(aa)5+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21a(aa)5+7a(aa)6+(aa)7
Apply the product rule to aa.
a3a+7a2a+21aa+35a+35aa+21aa5a5+7a(aa)6+(aa)7
Cancel the common factor of a.
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Factor a out of 21a.
a3a+7a2a+21aa+35a+35aa+a⋅21a5a5+7a(aa)6+(aa)7
Factor a out of a5.
a3a+7a2a+21aa+35a+35aa+a⋅21a5a⋅a4+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+35a+35aa+a⋅21a5a⋅a4+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a+35aa+21a5a4+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21a5a4+7a(aa)6+(aa)7
Combine 21 and a5a4.
a3a+7a2a+21aa+35a+35aa+21a5a4+7a(aa)6+(aa)7
Simplify the numerator.
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Rewrite a5 as (a5)12.
a3a+7a2a+21aa+35a+35aa+21a5a4+7a(aa)6+(aa)7
Rewrite a5 as (a2)2a.
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Factor out a4.
a3a+7a2a+21aa+35a+35aa+21a4aa4+7a(aa)6+(aa)7
Rewrite a4 as (a2)2.
a3a+7a2a+21aa+35a+35aa+21(a2)2aa4+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21(a2)2aa4+7a(aa)6+(aa)7
Pull terms out from under the radical.
a3a+7a2a+21aa+35a+35aa+21a2aa4+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21a2aa4+7a(aa)6+(aa)7
Cancel the common factor of a2 and a4.
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Factor a2 out of 21a2a.
a3a+7a2a+21aa+35a+35aa+a2(21a)a4+7a(aa)6+(aa)7
Cancel the common factors.
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Factor a2 out of a4.
a3a+7a2a+21aa+35a+35aa+a2(21a)a2a2+7a(aa)6+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+35a+35aa+a2(21a)a2a2+7a(aa)6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a+35aa+21aa2+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7a(aa)6+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7a(aa)6+(aa)7
Apply the product rule to aa.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa6a6+(aa)7
Rewrite a6 as a3.
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Use axn=axn to rewrite a as a12.
a3a+7a2a+21aa+35a+35aa+21aa2+7a(a12)6a6+(aa)7
Apply the power rule and multiply exponents, (am)n=amn.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa12⋅6a6+(aa)7
Combine 12 and 6.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa62a6+(aa)7
Cancel the common factor of 6 and 2.
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Factor 2 out of 6.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa2⋅32a6+(aa)7
Cancel the common factors.
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Factor 2 out of 2.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa2⋅32(1)a6+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa2⋅32⋅1a6+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa31a6+(aa)7
Divide 3 by 1.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3a6+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3a6+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3a6+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3a6+(aa)7
Cancel the common factor of a3 and a6.
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Multiply by 1.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3⋅1a6+(aa)7
Cancel the common factors.
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Factor a3 out of a6.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3⋅1a3a3+(aa)7
Cancel the common factor.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3⋅1a3a3+(aa)7
Rewrite the expression.
a3a+7a2a+21aa+35a+35aa+21aa2+7a1a3+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7a1a3+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7a1a3+(aa)7
Multiply 7a1a3.
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Combine 1a3 and 7.
a3a+7a2a+21aa+35a+35aa+21aa2+7a3a+(aa)7
Combine 7a3 and a.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+(aa)7
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+(aa)7
Apply the product rule to aa.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a7a7
Simplify the numerator.
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Rewrite a7 as (a7)12.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a7a7
Rewrite a7 as (a3)2a.
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Factor out a6.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a6aa7
Rewrite a6 as (a3)2.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+(a3)2aa7
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+(a3)2aa7
Pull terms out from under the radical.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a3aa7
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a3aa7
Cancel the common factor of a3 and a7.
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Factor a3 out of a3a.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a3(a)a7
Cancel the common factors.
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Factor a3 out of a7.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a3(a)a3a4
Cancel the common factor.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+a3aa3a4
Rewrite the expression.
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+aa4
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+aa4
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+aa4
a3a+7a2a+21aa+35a+35aa+21aa2+7aa3+aa4
Simplify ( square root of a+1/( square root of a))^7

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