Question

The value of $p^{-1}\cdot q\cdot q^{-1}\cdot r\cdot r^{-1}\cdot p$ is
(a) –1
(b) 0
(c) 1
(d) 2

Answer 1

Given expression is $p^{-1}\cdot q\cdot q^{-1}\cdot r\cdot r^{-1}\cdot p$
Using the rule of $a^m\times a^n=a^{m+n}$
$\Rightarrow p^{-1}\cdot q\cdot q^{-1}\cdot r\cdot r^{-1}\cdot p=p^{(-1+1)}\cdot q^{(-1+1)}\cdot r^{(1-1)}$
$=p^0\cdot q^0\cdot r^0$
$=1$ as $a^0=1$ for any non zero of a.
Hence, the correct option is (c).