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`

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

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

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

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