Question

${\left(\frac{x^a}{x^b}\right)}^c\times {\left(\frac{x^b}{x^c}\right)}^a\times {\left(\frac{x^c}{x^a}\right)}^b$ is equal to

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

The correct option is C 1

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

= $\frac{x^{ac}}{x^{bc}}\times \frac{x^{ba}}{x^{ca}}\times \frac{x^{cb}}{x^{ab}}$

= $x^{ac-bc}\times x^{bc-ca}\times x^{cb-ab}$

= $x^{(ac-bc+ba-ca+cb-ab)}$

= $x^0=1$