How do you simplify this equation?: (x^1/4 y^-1/3)`/( x^-1/2 y^3)`  

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oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on

`(x^(1/4)y^(-1/3))/((x^(-1)/2)y^3)=` `(2x^(1/4)y^(-1/3))/(x^(-1)y^3)=` `2x^(1/4+1)y^(-1/3-3)` `=2x^(5/4)y^(-10/3)` `=2(x root(4)(x))/(y^3 root(3)(y))`

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

We know

`x^(-m)=1/x^m`

`x^m/x^n=x^(m-n)`  ,

we have given

`(x^(1/4)y^(-1/3))/(x^(-1)/2y^3)`

`{x^(1/4)x^1y^(-1/3)y^(-3)}/(1/2)`

`=2x^(1/4+1)y^(-1/3-3)`

`=2x^(5/4)y^(-10/3)`

`=(2x^(5/4))/(y^(10/3))`

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