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`root(6)((((x^-6)*(y^3))/((x^2)*(y^5)))^2)/(x/(y^-1))` Simplify the expression.  

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phanpal999 | Student, Grade 8 | Salutatorian

Posted April 7, 2013 at 9:01 AM via web

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`root(6)((((x^-6)*(y^3))/((x^2)*(y^5)))^2)/(x/(y^-1))`

Simplify the expression.

 

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pramodpandey | College Teacher | Valedictorian

Posted April 7, 2013 at 9:20 AM (Answer #1)

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`((x^(-6)y^3)/(x^2y^5))^2=(x^(-6-2)y^(3-5))^2`

`(x^(-8)y^(-2))^2=x^(-8xx2)y^(-2xx2)`

`=x^(-16)y^(-4)`

`root6(((x^(-6)y^3)/(x^2y^5))^2)=(x^(-16)y^(-4))^(1/6)`

`=x^(-16xx(1/6))y^(-4xx(1/6))`

`=x^(-8/3)y^(-2/3)`

`` `root6(((x^(-6)y^3)/(x^2y^5))^2)/(x/y^(-1))=(x^(-8/3)y^(-2/3))/(x/y^(-1))`

`=(x^(-8/3)y^(-2/3))/(xy)`

`=x^(-8/3-1)y^(-2/3-1)`

`=x^(-11/3)y^(-5/3)`

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