Question

Find the value of : $\frac{x^{a(b-c)}}{x^{b(a-c)}}÷(\frac{x^b}{x^a}{)}^c$

• A. a
• B. 0
• C. b
• D. 1

Answer 1

The correct option is D

1

Given $\frac{x^{a(b-c)}}{x^{b(a-c)}}÷(\frac{x^b}{x^a}{)}^c$

$\Rightarrow \frac{x^{(ab-ac)}}{x^{(ba-bc)}}÷(\frac{x^b}{x^a}{)}^c$

$\because a^m\times a^n=(a{)}^{m+n}$ and $\frac{\left(a^m\right)}{\left(a^n\right)}$ = $a^{m-n}$

$\Rightarrow x^{ab-ac-ab+bc}÷(x^{b-a}{)}^c$

$\Rightarrow x^{ab-ac-ab+bc}÷x^{bc-ac}$ ($using,(a^n{)}^m=(a{)}^{m\times n}$)

$\Rightarrow \frac{x^{ab-ac-ab+bc}}{x^{bc-ac}}$

$\Rightarrow x^{ab-ac-ab+bc-bc+ac}$ ($using,\frac{\left(a^m\right)}{\left(a^n\right)}$ = $a^{m-n}$)

$\Rightarrow x^0=1$