The powers n and m are NOT equal to the stoichiometric coefficients a and b in the reaction equation.
The powers n and m are called the order of A and B, respectively. For n = 0, the reaction is zeroeth order in A. For n = 1, the reaction is first order in A. For n = 2, the reaction is second order in A. The reaction order is the sum of n plus m. The overall reaction could be first or second order. (Third order reactions are possible but very rare.)
As an example, consider an expression in the following equation: |