" 12.Simplify "root(4)(81x^(8)y^(4)z^(16))

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)))

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

Simplify (2x+3y+4z)^2=

Simplify: (15x^(5)y^(-2)z^(4))/(5x^(3)y^(-3)z^(2))

Simplify: (x+y-2z)^(2)-x^(2)-y^(2)-3z^(2)+4xy

Prove that : If |x| is so small that x^(4) and higher powers of x may be neglected, then find the approximate value of root(4)(x^(2).+81)-root(4)(x^(2)+16).

Simplify (81)^(0.16) xx (81)^(0.09)

Simplify (81x^(4)-16x^(2)+32x-16)/(9x^(2)-4x+4)

Simplify (81x^(4)-16x^(2)+32x-16)/(9x^(2)-4x+4)