Recommender systems serves as an important technical asset in many modern companies. With the increasing demand for higher precision of the technology, more and more research and investment has been allocated to the field. One important sub-field of recommender systems that has been stagnating is context-aware recommender systems. Due to the difficulty of collecting input dataset, the amount of research on context-aware recommender systems is much less than other sub-fields of recommender systems. In this paper, we propose a new algorithm named PowerMat to tackle the context-aware recommendation problem. We build our theory on matrix factorization and Zipf's law, and also more recent research work such as DotMat. We prove by experiments that our method achieves superior results to the classic matrix factorization algorithm and other context-aware recommender systems such as MovieMat+. In addition, by theoretical analysis, we show that our algorithm solves the cold-start problem for context-aware recommendation.