Question

If $p,q,n$ are three positive real numbers and $p>q$ then which of the following is correct.

Answer 1

Given that, $p>q$

$\Rightarrow \frac{1}{p}<\frac{1}{q}$
(using the property of inequality)
${\left(\frac{1}{p}\right)}^{\frac{1}{n}}<{\left(\frac{1}{q}\right)}^{\frac{1}{n}}$
Since $n$ is positive $\left(\frac{1}{n}\right)$ is also positive. So the inequality doesn't change when we raise both sides of the inequality with the positive number $\frac{1}{n}$.
Hence,
$p^{\frac{-1}{n}}<q^{\frac{-1}{n}}$
which is given by option (a).