The phrase “mighty prayer” indicates powerful, faith-filled communication with God. Elder Joseph B. Wirthlin (1917–2008) of the Quorum of the Twelve Apostles suggested ways we can evaluate and seek to improve the strength of our prayers:
“May I ask you today to consider the effectiveness of your prayers? How close do you feel to your Heavenly Father? Do you feel that your prayers are answered? Do you feel that the time you spend in prayer enriches and uplifts your soul? Is there room for improvement?
“There are many reasons our prayers lack power. Sometimes they become routine. Our prayers become hollow when we say similar words in similar ways over and over so often that the words become more of a recitation than a communication. This is what the Savior described as ‘vain repetitions’ (Matthew 6:7). Such prayers, He said, will not be heard. …
“Do your prayers at times sound and feel the same? Have you ever said a prayer mechanically, the words pouring forth as though cut from a machine? Do you sometimes bore yourself as you pray?
“Prayers that do not demand much of your thought will hardly merit much attention from our Heavenly Father. When you find yourself getting into a routine with your prayers, step back and think. Meditate for a while on the things for which you really are grateful” (“Improving Our Prayers,” in Brigham Young University 2002–2003 Speeches [2003], 160).