magistrate
dikastes denotes a person proposed or appointed to judge and rule over others in a dispute.
The two occurrences portray a person identified as judge in a challenge to Moses' authority: an opponent asks who made him ruler and judge, and the later retelling recalls that rejection before God sent Moses as ruler and redeemer.
Senses in use
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A judge whose authority is challenged · dominant
Both forms are accusative singular masculine nouns within the question about who made Moses "ruler and judge." In Acts 7:27 the question follows a man's rejection of Moses after he intervenes in wrongdoing; in Acts 7:35 the same challenge is recalled as the reason Moses had been rejected.
In the Anselm Project Bible: The APB presents the relevant clause as "Who made you ruler and judge over us?" in Acts 7:27 and recalls it as "Who made you ruler and judge?" in Acts 7:35., "judge" is treated as the clause's presentation rather than an isolated lexical equivalence.