Question

Find the value of ${\left(\frac{x^a}{x^b}\right)}^{\frac{1}{ab}}\times {\left(\frac{x^b}{x^c}\right)}^{\frac{1}{bc}}\times {\left(\frac{x^c}{x^a}\right)}^{\frac{1}{ca}}$

Answer 1

$=\left(\frac{x\frac{a}{ab}}{x\frac{6}{ab}}\right)\times \left(\frac{x\frac{b}{bc}}{x\frac{c}{bc}}\right)\times \left(\frac{x\frac{c}{ca}}{x\frac{a}{ca}}\right)$

$=\frac{x^{\frac{1}{b}}}{x^{\frac{1}{a}}}\times \frac{x^{\frac{1}{c}}}{x^{\frac{1}{b}}}\times \frac{x^{\frac{1}{a}}}{x^{\frac{1}{c}}}$

$=1$