However I do not understand where the values for m and n are coming from.
Technically they reflect stoichiometry of the reaction as it happens - which sometimes, in the case of very simple reactions, is eactly what the reaction equation says, but in most cases they reflect so called elementary reactions - which are simpler steps towards the full, complete process, described by the balanced equation.
From the data you have you shoudl be probably able to determine m and n. It is often not trivial to do so, see Rate equation page in wikipedia.