In short
Since Jesus did not cast out demons by Satan’s power, the logical conclusion is that he cast out demons by the Spirit of God (Matthew 12:28) or the finger of God (Luke 11:20)—both expressions referring to the power of God (Exodus 8:19).
As Jesus rejected the accusation that he performed his works by the power of Satan, the logical conclusion is that he casts out demons by the power of God. While Matthew 12:28 speaks of Jesus casting out demons by the Spirit of God, Luke 11:20 speaks of the finger of God instead. In the Old Testament both expressions are used to refer to the power of God (see Exodus 8:19).1
28 But if it is by the Spirit of God that I cast out demons, then the kingdom of God has come upon you.