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

${\left(\frac{x^a}{x^b}\right)}^a\times {\left(\frac{x^b}{x^a}\right)}^a\times {\left(\frac{x^a}{x^a}\right)}^b(x^{a-b}{)}^a\times (x^{b-a}{)}^a\times \left(x^{a-a}{)}^b\right(\because a^m÷a^n=a^{m-n})x^{a^2-ab}\times x^{ba-a^2}\times x^{ab-ab}(\because (a^m{)}^n=a^{mn})x^{a^2-ab+ba-a^2+ab-ab}(\because a^m\times a^n=a^{m+n})x^0=1$