Power is the sum of knowledge and material capacity to exercise your abilities (for example: money).
Authority can be of two types: irrational and rational (refering to the origin of that authority). The first is the kind of charismatic one, this authority could be defined as the capacity to exercise given by ritual, inmemorial or reverential respect. The second is usually given by a formality or systematic process constructed with that explicit end, so here the authority is not represented in the person but in the possition. Thus authority is just a kind or way of expression of power.