The power of God is shown by the birth of Jesus. Think about it this way. In Isaiah 53:1, he describes the "arm of the Lord" being revealed to mankind. The picture in the Hebrew is actually that of God strong-arming all His holiness, power, and deity into lowly, benign human form. It is an absolute miracle for a God of the Universe to confine Himself to such a humble vessel.
God continued to prove His power through the life of Jesus, as portrayed in the New Testament writings. The awesome incidents include Jesus' walking on the sea, stopping the storm and the waves, raising the dead, feeding the five thousand, healing the sick, casting out demons-the list goes on and on. In fact, the end of the book of John says that if all the miracles that Jesus did were put into books, the whole world couldn't contain them! That's a lot of miracles.
The Gospel is the power of God to everyone who believes. Belief is the key. Peter and his friends were poor, timid fishermen who preached the Gospel and felt the power of God in their lives, because they believed.
To quote Nehru, the first Prime Minister of India, "I do not know what the secret of the power is in the Gospel. It appears that when the worst sinners come to Jesus Christ, they become the best saints of the world."
God's power is exemplified in birth of Christ, and then again in the death of Christ. No earthly power could keep Jesus in the grave. He arose victoriously. The resurrection of Jesus is an act of God. As a result of Christ's resurrection, the resurrection of believers will follow. His forty days of life on earth after His resurrection and His ascension into heaven declared God's power then, now, and always. Great is our Lord, and mighty in power; His understanding is infinite (Psalm 147:5).