Nowhere to my knowledge does the New Testament record that Jesus laid his hands on anyone who needed to be set free from demons. On every occasion he simply commanded the evil spirits to leave and they did.
Authority and power go hand in hand. A police uniform and an upraised hand can bring the biggest truck to a screeching standstill. But along with that authority is the power to arrest anyone who would resist it.
“Summoning the Twelve, He gave them power and authority over all the demons, and to heal diseases.” (Luke 9:1) Jesus gave them the power to expel demons and the authority to act in his name. Their authority authorized their power. (Did you grasp that?)
“Look, I have given you authority to tread on serpents and scorpions and over all the power [authority] of the enemy, and nothing shall by any means harm you.” (Luke 10:19)
Think of this ‘twin’ ministry of authority and power as having two invisible letters on the palms of your hands. On one hand is a capital “A” for authority, and on the other is a capital “P” for power. If you are right handed, that will likely be the hand the Lord Jesus will use to heal the sick. When praying for those who are sick or injured you might lay both hands on them, using authority coupled with power to deliver their much-needed miracle of healing.
This may be likened to hunting with a double-barreled shotgun compared with a single-barreled one. Or the analogy of a police officer who backs up his authority with an application of physical force. Force is one thing; authority is another:it authorizes the right to exercise that power!