Question

State whether the statement is True or False.

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

• A. True
• B. False

Answer 1

The correct option is A True

L.H.S $=\left(\frac{x^a}{x^b}{)}^{\frac{1}{ab}}\right(\frac{x^b}{x^c}{)}^{\frac{1}{bc}}(\frac{x^c}{x^a}{)}^{\frac{1}{ca}}$
$=\left(\frac{x^{\frac{a}{ab}}}{x^{\frac{b}{ab}}}\right)\left(\frac{x^{\frac{b}{bc}}}{x^{\frac{c}{bc}}}\right)\left(\frac{x^{\frac{c}{ca}}}{x^{\frac{a}{ca}}}\right)$
$=\left(\frac{x^{\frac{1}{b}}}{x^{\frac{1}{a}}}\right)\left(\frac{x^{\frac{1}{c}}}{x^{\frac{1}{b}}}\right)\left(\frac{x^{\frac{1}{a}}}{x^{\frac{1}{c}}}\right)$
$=1$
$=$R.H.S