Notice in Matthew 10:1-5 Jesus clearly mentions, in no less than five times, that he was talking to the 12 apostles. In fact Jesus even mentions them by name should there be any confusion. Notice there was also territory restrictions, "to the house of Israel". This power was also for a limited time and it ended no later than Matthew 28, when Jesus commissions them to go the end of the world. Also these apostles were told to take nothing with them and rely totally on God's provision. They were not wealthy apostles traveling the world performing healing crusades and the like. (Mt 10:9-10)
And when he [Jesus] had called unto him his twelve disciples, he gave them power against unclean spirits, to cast them out, and to heal all manner of sickness and all manner of disease. Mt 10:1 Now the names of the twelve apostles are these;(v2) These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: Mt 10:5
Jesus has ALL authority not any man or self-proclaimed apostle or prophet today. The apostles of the first century, the 12 apostles were unique and a set permanent number, much like the 12 sons of Jacob. It was a unique office and the foundation of the church. Where a foundation is built, no more is to be laid.
Later in Matthew 28, Jesus commanded the apostles to go and teach ALL He commanded them. We see this all throughout the New Testament. No where did the apostles or Jesus teach believers to cast out demons or perform miracles. Mark 16 says “and these signs followed”. Jesus taught the apostles to teach us, to evangelize, baptize, disciple, pray and other things but never to go for the purpose of performing miracles and exorcisms. The signs and miracle were to authenticate the apostolic authority in the first century. In 2 Cor 12:12, Paul tells us that they were unique to the apostles, otherwise they would not be a sign of an apostle, if they were for all believers for all time.
Speaking to the eleven apostles Jesus says,” All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit, teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age.”
Matthew 28:18-20
In Luke 10 we have a similar situation. Jesus was speaking to specifically 70 disciples and NOT to all disciples for all time. These were specifically 70 disciples who were chosen to go to specific cities/places where “Jesus Himself was going (Lk. 10:1). They were not to be concerned with the essentials of life, but were to trust God.
Notice the 70 disciples had a beginning and an end to their mission. In Luke 10:17 they ended their mission. The places for Jesus to stay had been prepared. In verse 19 we have the perfect Greek tense used for the power Jesus gave to the disciples. The Greek perfect tense describes a completed action, which this was, that also produces results that are still in effect all the way up to the present, which they were.
Both Matthew 10 and Luke 10 describe missions that had specific parameters and instructions that also had an end. They are not continued missions for the Church today. Matthew 10 was only for the remnant Jews. This changes in Matthew 28 when Jesus gives a new command to the Apostles.
Mark 16 and the gifts of the Spirit are a separate subject. They will be addressed more closely in the future.