On simplification `[(x)^(ab)/(x)^(a^2+b^2)]^(a+b)**[(x)^(b^2+c^2)/(x)^(bc)]^(b+c)**[(x)^(ca)/(x)^(c^2+a^2)]^(c+a)` reduces to

On simplification [((x)^(ab))/((x)^(a^(2)+b^(2)))]^(a+b)*[((x)^(b^(2)+c^(2)))/((x)^(bc))]^(b+c)*[((x)^(ca))/((x)^(c^(2)+a^(2)))]^(c+) reduces to

On simplification [((x)^(ab))/((x)^(a^(2)+b^(2)))]^(a+b)*[((x)^(b^(2)+c^(2)))/((x)^(bc))]^(b+c)*[((x)^(ca))/((x)^(c^(2)+a^(2)))]^(c+) reduces to

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))

(x^(a^2 + b^2)/x^(ab))^(a+b) (x^(b^2 + c^2)/x^(bc))^(b+c) (x^(c^2 + a^2)/x^(ac))^(a+c) = x^(2(a^3+b^3+c^3))

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) .

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 :

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))