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`

Explanation

To solve the equation

\[ \left(\frac{x^a}{x^b}\right)^{\frac{1}{ab}} \cdot \left(\frac{x^b}{x^c}\right)^{\frac{1}{bc}} \cdot \left(\frac{x^c}{x^a}\right)^{\frac{1}{ac}} = 1 \]

we will break it down step by step.

...