(ii)(x^((1)/(a-b)))^((1)/(a-c))(x^((1)/(b-c)))^((1)/(b-a))(x^((1)/(c-a)))^((1)/(c-b))=1

(x^((1)/(a-b)))^((1)/(a-c))(x^((1)/(b-c)))^((1)/(b-a))((1)/(x^(c-a)))^((1)/(c-b))

(x^((1)/(a-b)))^((1)/(a-c))xx(x^((1)/(b-c)))^((1)/(b-a))xx(x^((1)/(c-a)))^((1)/(c-b))

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

Simply (x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-a)))^(1/(b-c))xx(x^(1/(c -a)))^(1/(c-b))

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

Simplify : (x^((b+c)/(c-a)))^((1)/(a-b))xx(x^((c+a)/(a-b)))^((1)/(b-c))xx(x^((a+b)/(b-c)))^((1)/(c-a)) .

In each of the following cases show that (dy).(dx)=0 , when y = (x^(1/(c-a)))^(1/(b-a))xx(x^(1/(a-b)))^(1/(c-b))xx(x^(1/(b-c)))^(1/(a-c))

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(1/(a b))\ ((x^b)/(x^c))^(1/(b c))\ \ ((x^c)/(x^a))^(1/(a c))=1