I suppose there are many answers to this question...
I believe that the power of prayer is first felt inside of us. Prayer is a covenant and agreement between us and GOD... A TWO-WAY COMMUNICATION. It's like someone answering a phone call when the phone has been ringing for a long time and we're wondering if maybe we should just hang up and try again another time. Then a voice answers and simply says, "I'm here. I'm listening to you." Communication has been established!
God is always ready to respond to our call. He wants to establish strong in relationship with us. It is God's deepest desire and has been hoping for... that we may learn how to fully entrust to Him everything that we care about through prayers.
I believe that we experience the power of God when we are able to believe God's great ability and unlimited capability to make us overcome life's trials. It's also awesome to realize that even before we call upon Him, God is really the One Who's been reaching out for us all along... So, LET'S NEVER CEASE TO PRAY! GOD LONGS FOR IT.