" (iv) "(sqrt(x))^(-2/3)sqrt(y^(4))-:sqrt(xy^(-1/2))" (v) "root(5)(243x^(10)y^(5)z^(10))

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))

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

Assuming that x,y are positive real numbers, simplify each of the following: sqrt(x^(-2)y^(3))(ii)(x^(-2)*y^(-(1)/(2)))^(2)(sqrt(x^(-3)))^(5)( iv) sqrt((x))^(-(2)/(3))sqrt(y^(4))+sqrt(xy^(-(1)/(2)))root(3)(xy^(2))-:x^(2)y(vi)root(3)(x^(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)))

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

root4(x^(17/2)y^(5/2)sqrt(x^(5/2)sqrt(x^(-7)y^6)))=

(2)/(sqrt(3)+sqrt(5))+(5)/(sqrt(3)-sqrt(5))=x sqrt(3)+y sqrt(5)

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

Factorise : (i) (x-y)^(3)+(y-z)^(3)+(z-x)^(3) (ii) (x-2y)^(3)+(2y-4z)^(3)+(4z-x)^(3) (iv) (3sqrt(2)a-5sqrt(3)b)^(3)+(5sqrt(3)b-7sqrt(5)c)^(3)+(7sqrt(5)c-3sqrt(2)a)^(3) .

Factorise : (i) (x-y)^(3)+(y-z)^(3)+(z-x)^(3) (ii) (x-2y)^(3)+(2y-4z)^(3)+(4z-x)^(3) (iv) (3sqrt(2)a-5sqrt(3)b)^(3)+(5sqrt(3)b-7sqrt(5)c)^(3)+(7sqrt(5)c-3sqrt(2)a)^(3) .