We consider tractable representations of probability distributions and the polytime operations they support. In particular, we consider a recently proposed arithmetic circuit representation, the Probabilistic Sentential Decision Diagram (PSDD). We show that PSDD supports a polytime multiplication operator, while they do not support a polytime operator for summing-out variables. A polytime multiplication operator make PSDDs suitable for a broader class of applications compared to arithmetic circuits, which do not in general support multiplication. As one example, we show that PSDD multiplication leads to a very simple but effective compilation algorithm for probabilistic graphical models: represent each model factor as a PSDD, and then multiply them.