(sqrt(x))^(2/3)sqrt(y^(4))+sqrt(xy^(-1/2))

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)))

The value of f(x,y)=((4sqrt(x^(3)y)-4sqrt(x^(3)))/(sqrt(y)-sqrt(x))+(1+sqrt(xy))/(4sqrt(xy)))^(-2)(1+2sqrt((y)/(x))+(y)/(x))^((1)/(2)) when x=9,y=0.04

If x,y in R satisfy the equation x^(2)+y^(2)-4x-2y+5=0, then the value of the expression ((sqrt(x)-sqrt(y))^(2)+4sqrt(xy))/((x+sqrt(xy))) is

Solve (2)/(sqrt(x))+(3)/(sqrt(y))=2 ;(4)/(sqrt(x))+(3)/(sqrt(y))=2

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

If x,y in R satify the equation x^(2)+y^(2)-4x-2y+5=0, then the value of the expression [(sqrt(x)-sqrt(y))^(2)+sqrt(xy)]/(x+4sqrt(xy)) is sqrt(2)+1 b.(sqrt(2)+1)/(2) c.(sqrt(2)-1)/(2) d.(sqrt(2)+1)/(sqrt(2))

Solve: (2)/(sqrt(x))-(3)/(sqrt(y))=2 and (4)/(sqrt(x))-(9)/(sqrt(y))=-1

(2)/(sqrt(x))+(3)/(sqrt(y))=2 and (4)/(sqrt(x))-(9)/(sqrt(y))=-1

Show that: (x^((2)/(3))sqrt(y^(-2)))/(y^(2)sqrt(x^(-2)))times(y^(2)sqrt(x^(-2)))/(sqrt(x^((4)/(3))))=(1)/(y)