In introductory chemical kinetics, an elementary reaction is taken for instance $$\ce{A -> B}$$ Then, we go on to derive integrated rate kinetics equations for them by assuming $$\text{rate} = k [\ce{A}]^n$$
Could it possible in a more generic case that : $\text{rate}=k[\ce{A}]^n [\ce{B}]^m$ and the total order of the reaction be $m+n$? In other words, can the rate of reaction depend on both the molar concentrations of reactants and products independently?