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

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

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

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)))^((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^(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