Representation of non zero rational number

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I have seen the following representation of non zero rational numbers in course notes :

$$ \forall r\in\mathbb{Q}\setminus\{0\},\quad r = p^{k}\frac{m}{n}\quad k,m,n\in\mathbb{Z} $$

where $p$ is a prime number not dividing $m$ nor $n$. Where does it come from please ? I would like to know more on this (never studied arithmetic) but unable to find a ressource on this.

Thank you !