`sqrt(x^(-2)y^(3))`
`root(4)(root(3)(x^(2)))`

Evaluate lim_(xtooo) (sqrt(x^(2)+1)-root(3)(x^3+1))/(root(4)(x^(4)+1)-root(5)(x^(4)+1))

int\ (root(3)x)(root(5)(1+root(3)(x^4)))dx

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)

Evaluate the following limits : Lim_(x to oo) (sqrt(x^(2)+1)-root3(x^(3)-1))/(root4(x^(4)+1)-root5(x^(4)+1))

Evaluate lim_(xto2) (sqrt((x+7))-3sqrt((2x-3)))/(root(3)((x+6))-2root(3)((3x-5))).

Evaluate int(sqrt(1+root(3)(x)))/(root(3)(x^(2)))dx .

Evaluate: int root(3)(x)root(3)(1+root(3)(x^(4)))dx

lim_(xtooo) (2sqrt(x)+3root(3)(x)+4root(4)(x)+...+nroot(n)(x))/(sqrt((2x-3))+root(3)((2x-3))+...+root(n)((2x-3))) is equal to

lim_(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

Evaluate int(1)/(sqrt(e^(5x))root(4)((e^(2x)+e^(-2x))^(3))) .