For a large class of piecewise expanding maps of metric spaces we show the equidistribution of standard pairs at an exponential rate. As a corollary such systems have a unique absolutely continuous invariant measure with respect to which the system is mixing. We allow for unbounded, non-compact spaces, countably many branches and do not assume big images or the existence of a Markov structure. We show how to control the complexity growth of the dynamical partition of the map. Such control is necessary and crucial for systems that are not one-dimensional. Our method gives explicit estimates on the exponential rate of equidistribution.