4√81x^8y^16+√36x^4y^8
Answers
Step-by-step explanation:
Use n√ax=axnaxn=axn to rewrite √36x4y36x4y as (36x4y)12(36x4y)12.
4√81x16+(36x4y)12⋅8481x16+(36x4y)12⋅8
Use the power rule (ab)n=anbn(ab)n=anbn to distribute the exponent.
Apply the product rule to 36x4y36x4y.
4√81x16+(36x4)12y12⋅8481x16+(36x4)12y12⋅8
Apply the product rule to 36x436x4.
4√81x16+3612(x4)12y12⋅8481x16+3612(x4)12y12⋅8
Simplify the expression.
Rewrite 3636 as 6262.
4√81x16+(62)12(x4)12y12⋅8481x16+(62)12(x4)12y12⋅8
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
4√81x16+62(1/2)(x4)12y12⋅8481x16+62(12)(x4)12y12⋅8
Cancel the common factor of 22.
Cancel the common factor.
4√81x16+62(12)(x4)12y12⋅8481x16+62(12)(x4)12y12⋅8
Rewrite the expression.
4√81x16+61(x4)12y12⋅8
Simplify the expression.
Evaluate the exponent.
4√81x16+6(x4)12y12⋅8481x16+6(x4)12y12⋅8
Multiply the exponents in (x4)12(x4)12.
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
4√81x16+6x4(12)y12⋅8481x16+6x4(12)y12⋅8
Cancel the common factor of 22.
Factor 22 out of 44.
4√81x16+6x2(2)12y12⋅8481x16+6x2(2)12y12⋅8
Cancel the common factor.
4√81x16+6x2⋅212y12⋅8481x16+6x2⋅212y12⋅8
Rewrite the expression.
4√81x16+6x2y12⋅8481x16+6x2y12⋅8
Multiply 88 by 66.
4√81x16+48x2y12481x16+48x2y12
Factor 3x23x2 out of 81x16+48x2y1281x16+48x2y12.
Factor 3x23x2 out of 81x1681x16.
4√3x2(27x14)+48x2y1243x2(27x14)+48x2y12
Factor 3x23x2 out of 48x2y1248x2y12.
4√3x2(27x14)+3x2(16y12)43x2(27x14)+3x2(16y12)
Factor 3x23x2 out of 3x2(27x14)+3x2(16y12)3x2(27x14)+3x2(16y12).
4√3x2(27x14+16y12)43x2(27x14+16y12)
Rewrite 3x2(27x14+16y12)3x2(27x14+16y12) as x2⋅(3(27(x7)2+16y12))x2⋅(3(27(x7)2+16y12)).
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Reorder 33 and x2x2.
4√x2⋅3(27x14+16y12)4x2⋅3(27x14+16y12)
Rewrite x14x14 as (x7)2(x7)2.
4√x2⋅3(27(x7)2+16y12)4x2⋅3(27(x7)2+16y12)
Add parentheses.
4√x2⋅(3(27(x7)2+16y12))4x2⋅(3(27(x7)2+16y12))
Pull terms out from under the radical.
4(x√3(27(x7)2+16y12))4(x3(27(x7)2+16y12))
Multiply the exponents in (x7)2(x7)2.
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
4(x√3(27x7⋅2+16y12))4(x3(27x7⋅2+16y12))
Multiply 77 by 22.
4(x√3(27x14+16y12))
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