The question is, Let $\displaystyle n$ be a positive integer and let $\displaystyle D$ be the subset of all rational numbers of the form $\displaystyle \frac{a}{n^k}$ with $\displaystyle a \in \mathbb{Z}$ and $\displaystyle k$ any positive integer. Show that $\displaystyle D$ is an integral domain whose quotient field is isomorphic to the field of rational numbers.

So I have already shown that $\displaystyle D$ is an integral domain.

I am having issues proving that its quotient field is isomorphic to the field of rational numbers. I don't really even know where to start.

Anyhintswould be nice. I don't want a full proof I would like to do my own work. Just a little push in the right direction would be great.

Thank you!