Authority vs. Power
Jesus did not just send them forward into their world with empty hands. He provides them with all the tools that will be needed to bring in this harvest of souls. According to Matthew's account, Jesus "...gave them power" [10:1]. The New International Version employs a more definite word for "power." The term "authority" is utilized instead.
Let me try to explain it in this way: A policeman has the authority to stop a speeding car but does not have the power to do so. By virtue of the law officer's position and certification, he or she has the authority of the law of the land to stop a car that is speeding down a freeway. But, he or she does not have the ability to actually halt the vehicle through his or her physical power.
It is no different with the church today. We, too, are His disciples and have been entrusted with the authority to cast out demonic forces, heal the diseased, and preach the good news of Jesus the Christ. We cannot do these miraculous wonders of our own power and abilities. Jesus empowers us through the call of discipleship to go and complete these marvels through his name.