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

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

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

$=\left(x^{ab-ac-ab+bc}\right)÷(x^{b-a}{)}^c$
$[\because \frac{\left(a^m\right)}{\left(a^n\right)}$ = $a^{m-n}]$

$=x^{ab-ac-ab+bc}÷x^{bc-ac}$
$[\because (a^m{)}^n=\left(a{)}^{m\times n}\right]$

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

$=x^{ab-ac-ab+bc-bc+ac}$
$[\because \frac{\left(a^m\right)}{\left(a^n\right)}$ = $a^{m-n}]$$=x^0$

$=1$ $[\because a^0=1,a\ne 0]$