The value of `(x^a/x^b)^(a+b)*(x^b/x^c)^(b+c)*(x^c/x^a)^(c+a)` is

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

If f(x)=((x^2)/(x^b))^(a+b)*((x^b)/(x^c))^(b+c)*((x^c)/(x^a))^(c+a) , then f^(prime)(x) is equal to: (a) 1 (b) 0 (c) x^(a+b+c) (d) None of these

For any positive real number x , find the value of ((x^a)/(x^b))^(a+b)\ xx\ ((x^b)/(x^c))^(b+c)\ xx\ ((x^c)/(x^a))^(c+a)

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/(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

If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x-b)(x-c) is (a) a+b+c (b) (a-b)(b-c)(c-a) (c) 0 (d) None of these

Simplify: (i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^(c+a))/(x^b))^(c-a) (ii)\ ((x^l)/(x^m))^(1/(lm))\ xx\ ((x^m)/(x^n))^(1/(mn))\ xx\ \ ((x^n)/(x^l))^(1/(ln))

If x is a positive real number and the exponents are rational numbers, Find: ((x^a)/(x^b))^(a^2+b^2-a b). ((x^b)/x^c)^(b^2+c^2-b c). ((x^c)/(x^(a)))^(c^2+a^2-c a)

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