Question

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

Answer 1

$Wehave$

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

$=\frac{x^{a^2}}{x^{ba}}\times \frac{x^{ba}}{x^{a^2}}\times \frac{x^{ab}}{x^{ab}}$

$a=1$

${\left(\frac{x^a}{x^b}\right)}^a\times {\left(\frac{x^b}{x^a}\right)}^a\times {\left(\frac{x^a}{x^a}\right)}^b=1$