Simplify : `((x^a)/(x^b))^(a^2+b^2+ab)xx((x^b)/(x^c))^(b^2+c^2+bc)xx((x^c)/(x^a))^(c^2+a^2+ca)`.

Simplify : ((x^a)/(x^b))^(a^2+ab+b^2)xx((x^b)/(x^c))^(b^2+bc+c^2)xx((x^c)/(x^a))^(c^2+ca+a^2) .

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

Prove that: ((x^a)/(x^b))^(a^(2+a b+b^(2)))xx\ ((x^b)/(x^c))^(b^(2+b c+c^2))\ xx\ ((x^c)/(x^a))^(c^(2+c a+a^2))

The value ((x^a)/(x^b))^((a^2 + ab + b^2)) ((x^b)/(x^c))^((b^2 + bc + c^2))((x^c)/(x^a))^((c^2 + ca + a^2)) is :

Prove that: ((x^a)/(x^(b)))^(a^(2+a b+b^2))\ xx\ ((x^b)/(x^(c)))^(b^(2+b c+c^2))\ xx\ ((x^c)/(x^(a)))^(c^(2+c a+a^2))=1

Simplify : ((x^(a))/(x^(-b)))^(a^(2)-ab+b^(2))xx((x^(b))/(x^(-c)))^(b^(2)-bc+c^(2))xx((x^(c))/(x^(-a)))^(c^(2)-ca+a^(2))