Assuming that `x , y , z` are positive real numbers, simplify each of the following: `(i)\root(3)(x y^2) \ -:\x^2y` `(ii)\ root(4)root(3)(x^2)`

Explanation

(i) `root(3)(xy^2)-:x^2y`
`=(xy^2)^1/3-:x^2y`
`=x^1/3y^2/3-:x^2y`
`=x^(1/3-2)y^(2/3-1)`
`=x^(-5/3)y^(-1/3)`

(ii) `root(4)root(3)(x^2)`
`=((x^2)^(1/3))^(1/4)`
`=x^(2xx1/3xx1/4)`
`=x^(2/12)`
`=x^(1/6)`