to exercise authority over people: to rule others, in both its uses picturing the heavy-handed, top-down way worldly rulers throw their weight around
This word appears only twice in the Bible, and both times in the same scene: Jesus contrasting how "the rulers of the nations" wield power with how his followers should lead by serving (Matthew 20:25, Mark 10:42). It is essentially a word coined in the Gospels. It shows up nowhere in the Greek Old Testament and in no known Greek writing before the New Testament, which is why its exact shade of meaning is debated.
It is built from a common verb meaning "to exercise authority" (ἐξουσιάζω) with the small word "down" attached to the front. Jesus pairs it with a twin verb, κατακυριεύω ("to lord over"), and the two together hammer a single idea: powerful people using their position to bear down on those beneath them.
What Jesus criticizes is not authority itself but the manner of it. In the same breath he tells his disciples that true greatness among them looks like serving, not ruling. Scholars debate whether the added prefix builds a domineering flavor into the word itself or simply intensifies it, leaving the negative edge to come from the surrounding contrast ("it shall not be so among you"). Either way, the point of the sentence is the same.
Disputed
Whether the κατά- prefix gives the verb a built-in pejorative sense (to domineer, tyrannize) or is merely intensive or perfective, with the negative force supplied by the Gospel context rather than the lexeme.
- contestedThe κατά- prefix carries a downward, adversative, bearing-down force, so the verb itself connotes domineering or tyrannical rule.; R. T. France, The Gospel of Matthew (NICNT), Eerdmans, 2007, 759-760; BDAG, s.v. κατεξουσιάζω ("exercise authority, perhaps tyrannize")
- contestedThe κατά- prefix is intensive or perfective (fully exercise authority), functionally equivalent to the simplex ἐξουσιάζω; any negative sense arises from context, not the word. The parallel κατακυριεύω describes positive dominion in Gen 1:28 LXX and Ps 110:2 LXX, and 1 Pet 5:3 turns negative only by explicit contrast.; J. H. Moulton, A Grammar of New Testament Greek, vol. 1: Prolegomena, 3rd ed., T&T Clark, 1908, 111-115; Moisés Silva, Biblical Words and Their Meaning, rev. ed., Zondervan, 1994, 44-51; Louw & Nida, Greek-English Lexicon Based on Semantic Domains, 2nd ed., 1989, 37.48