What is the meaning of "Subhana Rabbi al-Adheem" (Glory be to my Lord, the Most Great) and "Subhana Rabbi al-A'la" (Glory be to my Lord, the Most High), and is it obligatory to ponder their meanings or the majesty and loftiness of Allah during Rukoo' (bowing) and Sujood (prostration)?

The meaning of Tasbih (glorification) is to declare Allah Almighty free from all imperfections and deficiencies. So, saying "SubhanAllah" (Glory be to Allah) means declaring Him free from every imperfection and deficiency. The meaning of "Al-Atheem" (the Most Great) is the One possessing ultimate greatness, and the meaning of "Al-A'la" (the Most High) is the One who is exalted in His essence and attributes. The worshipper must ponder over the meanings of the Adhkar (remembrances) and actions performed in prayer. In Ruku' (bowing) and Sujud (prostration), it is legislated to glorify Allah Almighty through word, action, and heart, by saying "Subhana Rabbiyal-Atheem" (Glory be to my Lord, the Most Great) in Ruku' and "Subhana Rabbiyal-A'la" (Glory be to my Lord, the Most High) in Sujud. Pondering over the meanings of the Adhkar leads to contemplating the greatness and majesty of Allah, but this should not be exaggerated, lest it become a whisper from Satan that distracts the worshipper from their prayer.