I have a question about this proof that shows the relationship between the rate constant and the equilibrium constant. In this proof, the assumption is that the reaction is (a+b)th order (forward) and (c+d)th order (reverse). I had always thought reaction orders are empirically determined (and not necessarily whole numbers); can one simply add the stoichiometric coefficients like this? If not, how does one show that equilibrium constant is a ratio of the rate constants since the equilibrium constant requires the concentrations raised to the order of the species' stoichiometric coefficient?

I have a question about this proof that shows the relationship between the rate constant and the equilibrium constant. In this proof, the assumption is that the reaction is $(a+b)$th order in the forward direction and $(c+d)$th order in the reverse direction. 

I had always thought reaction orders are empirically determined (and not necessarily whole numbers); can one simply add the stoichiometric coefficients like this? If not, how does one show that equilibrium constant is a ratio of the rate constants since the equilibrium constant requires the concentrations raised to the order of the species' stoichiometric coefficient?