Question

Simplify
${\left(\frac{x^a}{x^b}\right)}^c\times {\left(\frac{x^b}{x^c}\right)}^a\times {\left(\frac{x^c}{x^a}\right)}^b$

Answer 1

Now,

${\left(\frac{x^a}{x^b}\right)}^c\times {\left(\frac{x^b}{x^c}\right)}^a\times {\left(\frac{x^c}{x^a}\right)}^b$

$=(x^{a-b}{)}^c\times (x^{b-c}{)}^a\times (x^{c-a}{)}^b$

$=x^{ac-bc+ab-ac+bc-ab}$

$=x^0$

$=1$.