Question

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

• A. $1$
• B. $-1$
• C. $0$
• D. abc

Answer 1

The correct option is A $1$

${\left(\frac{x^b}{x^a}\right)}^{\frac{1}{bc}}\cdot {\left(\frac{x^c}{x^a}\right)}^{\frac{1}{ca}}\cdot {\left(\frac{x^a}{x^b}\right)}^{\frac{1}{ab}}$
$={\left(x^{b-c}\right)}^{\frac{1}{bc}}\cdot {\left(x^{c-a}\right)}^{\frac{1}{ca}}\cdot {\left(x^{a-b}\right)}^{\frac{1}{ab}}$
$=x^{\frac{b-c}{bc}}\cdot x^{\frac{c-a}{ca}}\cdot x^{\frac{a-b}{ab}}$
$=x^{\frac{1}{c}-\frac{1}{b}}\cdot x^{\frac{1}{a}-\frac{1}{c}}\cdot x^{\frac{1}{b}-\frac{1}{a}}$
$=x^{\frac{1}{c}-\frac{1}{b}+\frac{1}{a}-\frac{1}{c}+\frac{1}{b}+\frac{1}{a}}$
$=x^o=1$