Approximate computing can efficiently trade accuracy for power savings, thus optimizing the power for applications that don't require exact solutions. This tradeoff has been studied in recent years across several implementation technologies, but mostly focused on approximations on a specific system layer. This thesis investigates how approximations interact at different layers and affect accuracy and power. We present a hierarchical model that attempts to analytically define levels of approximations, such that we can model the effects of approximations at multiple layers, as a function of a priori knowledge of the approximations' effects at each layer. We evaluate the validity of our model for an image processing application on a RISC-V simulator across two layers. The results indicate while type A model predicts accuracy pessimistically, type B model anticipates both power and accuracy with >98% accuracy. We discuss work towards improving this model and evaluating it across more comprehensive empirical results.