​ Simplify: (x^a/x^b)^a x (x^b/x^a)^a x (x^a/x^a)^b ​

Question

Simplify: \((\frac {x^a}{x^b})^a \times (\frac {x^b}{x^a})^a \times (\frac {x^a}{x^a})^b\)

(x^a/x^b)^a x (x^b/x^a)^a x (x^a/x^a)^b

Answer 1

Given \((\frac {x^a}{x^b})^a \times (\frac {x^b}{x^a})^a \times (\frac {x^a}{x^a})^b\) = \((\frac {x^a}{x^b} \times \frac {x^b}{x^a})^a \times (1)^b\)

[∵ a^m × b^m = (ab)^m]

= 1^a x 1^b = 1^a+b = 1