Question

The value of ${\left(\frac{x^b}{x^c}\right)}^{\frac{1}{bc}}{\left(\frac{x^c}{x^a}\right)}^{\frac{1}{ca}}{\left(\frac{x^a}{x^b}\right)}^{\frac{1}{ab}}$ on
Simplifying is

• A. x
• B. 1/x
• C. 1
• D. -1

Answer 1

The correct option is C 1

${\left(\frac{x^b}{x^c}\right)}^{\frac{1}{bc}}{\left(\frac{x^c}{x^a}\right)}^{\frac{1}{ca}}{\left(\frac{x^a}{x^b}\right)}^{\frac{1}{ab}}=\left(x^{b-c}{)}^{\frac{1}{bc}}\right(x^{c-a}{)}^{\frac{1}{ca}}(x^{a-b}{)}^{\frac{1}{ab}}$
$=x^{\frac{b-c}{bc}+\frac{c-a}{ca}+\frac{a-b}{ab}}$
$=x^{\frac{ab-ac+bc-ab+ac-bc}{abc}}$
$=x^0=1$
Option C is correct.