`(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))

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

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))

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))

(x^(b)/x^(c ))^(1/(bc))xx(x^(c )/x^(a))^(1/(ca))xx(x^(a)/x^(b))^(1/(ab))

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)) .

The value of ((x^(a))/(x^(b)))^((1)/(ab)) xx ((x^(b))/(x^(c)))^((1)/(bc)) xx ((x^(c))/(x^(a)))^((1)/(ca)) is equal to

Show that (x^(b-c))^((1)/(bc))xx(x^(c-a))^((1)/(ca))xx(x^(a-b))^((1)/(ab))=1 .