Question

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

• A. $x^{abc}$
• B. $abc$
• C. $1$
• D. $0$

Answer 1

The correct option is C $1$

We need to find value of ${\left(\frac{x^a}{x^b}\right)}^{\frac{1}{ab}}{\times \left(\frac{x^b}{x^c}\right)}^{\frac{1}{bc}}\times {\left(\frac{x^c}{x^a}\right)}^{\frac{1}{ca}}$

$=\frac{{\left(x^a\right)}^{\frac{1}{ab}}}{{\left(x^b\right)}^{\frac{1}{ab}}}\times \frac{{\left(x^b\right)}^{\frac{1}{bc}}}{{\left(x^c\right)}^{\frac{1}{bc}}}\times \frac{{\left(x^c\right)}^{\frac{1}{ca}}}{{\left(x^a\right)}^{\frac{1}{ca}}}=\frac{x^{\frac{1}{b}}}{x^{\frac{1}{a}}}\times \frac{x^{\frac{1}{c}}}{x^{\frac{1}{b}}}\times \frac{x^{\frac{1}{a}}}{x^{\frac{1}{c}}}=1$