ekzekuti

A dark word, and the useful thing to say about it is a boundary rather than a definition. In Esperanto ekzekuti means to put a condemned person to death, and only that. The English verb does two jobs, and a learner arriving from English will naturally reach for ekzekuti when they mean to carry out a plan. Do not. The dictionaries are consistent here: the reference works define ekzekuti as killing under a judicial sentence, and the carrying-out sense lives in other words.

Which words. To carry out a plan, an order or a promise is plenumi, which is the everyday choice and is itself a nice piece of Esperanto (plena plus -um-). To put a decision into effect more formally is efektivigi. And there is a separate legal noun, ekzekucio, for the enforcement of a court's judgement, the seizure and the bailiff rather than the scaffold; it looks like it belongs to ekzekuti and in origin it does, but it is a distinct entry and does not license the general sense.

The computing use you will meet online (ekzekuti programon, to run a program) is a modern extension by analogy with English, and it is understood, but the careful term is ruli and the careful writer uses it. The etymology explains the whole mess in one line: Latin exsequi meant to follow a thing through to the end, which is what an executor of a will does, what an executive branch does, and, in the grimmest reading, what an executioner does. English kept every branch; Esperanto pruned back to one.