Solution
= Solution
This relation is reflexive because choosing $n=1$ gives $|x/x|=1$. It need not be symmetric: take positive real numbers $y=e$ and $x=e^2$. Then $|x/y^2|=1$ is rational, so $x\sim y$. But
$$
\left|\frac{y}{x^m}\right|=e^{1-2m}
$$
is transcendental, hence irrational, for every integer $m\geq1$. Thus $y\not\sim x$, and the relation is not an equivalence relation.