Prove that : `((x^a)/(x^b))^(a+b-c)((x^b)/(x^c))^(b+c-a)((x^c)/(x^a))^(c+a-b)=1`

If x is a positive real number and the exponents are rational numbers, show that: ((x^a)/(x^b))^(a+b-c)\ ((x^b)/(x^c))^(b+c-a)((x^c)/(x^a))^(c+a-b)=1

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

Prove that: ((x^(a))/(x^(b)))^(c)x((x^(b))/(x^(c)))^(a)x((x^(c))/(x^(a)))^(b)=1

If x is a positive real number and the exponents are rational numbers,show that: ((x^(a))/(x^(b)))^(a+b-c)((x^(b))/(x^(c)))^(b+c-a)((x^(c))/(x^(a)))^(c+a-b)=1

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

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

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

((x^(a))/(x^(b)))^(a+b-c)*((x^(b))/(x^(c)))^(b+c-a)*((x^(c))/(x^(a)))^(c+a-b)= a.1 b.x^(abc) c.x^(ab+bc+ca) d.x^(a+b+c)

Differentiate ((x^(a))/(x^(b)))^(a+b)*((x^(b))/(x^(c)))^(b+c)*((x^(c))/(x^(a)))^(c+a) with respect to x.