root(5)(x^(4))root(4)(x^(3)root(3)(x^(2)sqrt(x)))

Assuming that x, y, z are positive real numbers, simplify each of the following . (i) sqrt(x^(3)y^(-2)) (ii) (x^(-2//3) y^(-1//2))^(2) (iii) ((x^(-4))/(y^(-10)))^((5)/(4)) (iv) (root4(81 x^(8)y^(8)z^(16))) div (root3(27x^(3)y^(6)z^(9))) (v) root5(x^(4) root4(x^(3)root3(x^(2)sqrt(x)))) (vi) ((sqrt(x))^(-(2)/(3)) sqrt(y^(4))) div (sqrt(xy^(-(1)/(2))) sqrt(x^(-2)y^(3)))

Evaluate: int((1)/(root(3)(x)+root(4)(x))+(ln(1+root(6)(x))/(root(3)(x)+sqrt(x)))dx

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

int(root(3)(x^2)-root(4)(x))/(sqrt(x))dx

int(root(3)x ^(2)+root(4)x+root(3)x)/(sqrtx)dx=

root(5)(x^(8).sqrt(x^(6).sqrt(x^(-4))

sqrt(root(x)(2^(x))root(x^(2))(3^(x^(3)))root(x^(2))(6^(x^(6)))root(x^(4))(9^(x^(10)))) =

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

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

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