Although their mission entailed more than exorcism (healing and preaching are mentioned later), it is mentioned first. Jesus gave the Twelve the authority he had, to continue what he did. To have authority over the unclean spirits was a sign that God the Father really sent Christ to this world (see John 11:42, Mark 1:27). Now this authority is given by Jesus to the Twelve. They were commissioned.1 When his mission was extended through the disciples, it meant not only the content and manner, but also his authority to be able accomplish it.
7 And he called the twelve and began to send them out two by two, and gave them authority over the unclean spirits.