Question

Evaluate ${\left(\frac{x^a}{x^{-b}}\right)}^{a-b}.{\left(\frac{x^b}{x^{-c}}\right)}^{b-c}.{\left(\frac{x^c}{x^{-a}}\right)}^{c-a}$

• A. 8
• B. 4
• C. 2
• D. 1

Answer 1

The correct option is D 1

${\left(\frac{x^a}{x^{-b}}\right)}^{a-b}.{\left(\frac{x^b}{x^{-c}}\right)}^{b-c}.{\left(\frac{x^c}{x^{-a}}\right)}^{c-a}$

$=(x^{(a+b)}{)}^{(a-b)}.(x^{(b+c)}{)}^{(b-c)}.(x^{(c+a)}{)}^{(c-a)}$

$=x^{a^2-b^2}.x^{b^2-c^2}.x^{c^2-a^2}$

$=x^{a^2-b^2+b^2-c^2+c^2-a^2}$

$=x^0$

$=1$