Assuming that `x ,\ y ,\ z` are positive real numbers, simplify each of the following: `(sqrt(x))^(-2/3)\ sqrt(y^4)-:\ sqrt(x y^(-1/2))` (ii) `root(5)(243\ x^(10)y^5z^(10))`

Explanation

1408709 (i) `(sqrt(x))^(-2/3)\ sqrt(y^4)-:\ sqrt(x y^(-1/2))`
`=(x^(-2/3xx1/2)xxy^2)/(x^(1/2)y^(-1/4))`
`=(x^(-1/3)xxy^2)/(x^(1/2)y^(-1/4))`
`=x^(-1/3-1/2)xxy^(2+1/4)`
`=x^(-5/6)xxy^(9/4)`
`=y^(9/4)/x^(5/6)`

(ii) `root(5)(243\ x^(10)y^5z^(10))`
`=root(5)(3^5\ (x^2)^(5)y^5(z^2)^(5))`
`=3x^2y^5z^2`