The key word in this inspiring teaching is “authority,” which is the Greek, exousia. It means, “the power of rule or government (the power of him whose will and commands must be submitted to by others and obeyed)”.
As you probably know, Jesus said, “Whoever believes in me will do the works I have been doing. When he sent out the 70 disciples, he said: “I have given you authority to trample on snakes and scorpions and to overcome all the power of the enemy. They believed him, and did the same works he did. When he interrupted Saul on the road to Damascus, the Lord said: “I am sending you to open their eyes and turn them from darkness to light, and from the authority of Satan to God.”
Jesus never prayed that a demon would come out, nor are we are told to do so. Ditto for sickness. He simply exercised the authority God had given him to deal with it. Romans and Ephesians tell us that you and I died with Christ, were buried with him, raised with him, and then seated with him. We now sit in a position of authority IN CHRIST. The question is: Will we choose to use that authority?