Question

Simplify $\frac{x^a}{x^b}\times \frac{x^b}{x^a}\times \frac{x^a}{x^b}$.

• A. $x^{a+b}$
• B. $x^{a-b}$
• C. $x^{ab}$
• D. $x^{b-a}$

Answer 1

The correct option is B $x^{a-b}$

Given $\frac{x^a}{x^b}\times \frac{x^b}{x^a}\times \frac{x^a}{x^b}$
Using the Law of Exponents,
$\frac{a^m}{a^n}=a^{m-n}$
$⟹x^{a-b}\times x^{b-a}\times x^{a-b}$

We know that,
$a^m\times a^n=a^{m+n}$
$⟹x^{(a-b)+(b-a)+(a-b)}=x^{a-a+a-b+b-b}=x^{a-b}$
$⟹\frac{x^a}{x^b}\times \frac{x^b}{x^a}\times \frac{x^a}{x^b}=x^{a-b}$