Question

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

• A. X
• B. $\frac{1}{x}$
• C. 1
• D. -1

Answer 1

The correct option is C 1

${\left(\frac{x^b}{x^c}\right)}^{1/bc}.{\left(\frac{x^c}{x^a}\right)}^{1/ca}{\left(\frac{x^a}{x_b^b}\right)}^{1/ab}$

$\Rightarrow \frac{x^{-c}}{x^{-b}}.\frac{x^{-a}}{x^{-c}}.\frac{x^{-b}}{x^{-a}}$

$\Rightarrow 1$