Prayer is powerful -- but only as powerful as the person you pray to. Our God and creator who spoke the universe into existence and sent His Son into the world as a redeemer is all-powerful, loving, and good. He has promised to hear the prayers of His people. He has placed some conditions on answered prayer, and He is rarely on the same time table as we, but we have His word that He will hear us, and we know He is able. Thus, "The effectual fervent prayer of a righteous man availeth much."
Prayers made to saints, guardian angels, ancestors, or a vague higher power may be powerful too --- as powerful as the demon who receives them. The devil is not all-powerful, and he does not promise to answer prayer. He certainly gives no assurance that he has our well-being at heart. Nonetheless, the devil has real power, and if it suits his purposes, he may answer prayer in a mighty and powerful way.
When we pray, we must be very clear who we are praying to and in whose name we pray. If we pray in our own name to anyone who has power to help us, we may get an answer, but it may not be from God. Those of us who love the Lord Jesus pray to the Father in His name. We know the power of that prayer, but its power is not in itself. The power is in the one true God to whom we pray. He is not only all-powerful. He is also holy and good. Let us be careful not to confuse our honor to Him for His goodness in answering our prayers with what the world gives to prayer itself without defining who is being prayed to. Let us make a distinciton between "the power of prayer" and the power of God to whom we pray in the name of His Son the Lord Jesus Christ.