((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))

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))

((x^(a))/(x^(-b)))^(a^(2)-ab+b^(2))times((x^(b))/(x^(-c)))^(b^(2)-bc+c^(2))times((x^(c))/(x^(-a)))^(c^(2)-ca+a^(2))

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))

Prove that: ((x^(a))/(x^(b)))^(a)-2+ab+b^(2)x((x6b)/(x^(c)))^(b)-2+bc+c^(2)x((x^(c))/(x^(a)))^(c)-2+ca+a^(2)

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

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))

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a^2+a b+b^2)((x^b)/(x^c))^(b^2+b c+c^2)((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) .

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