How long did ancient Greeks' power last?

There was no ancient Greek empire. Greece (Hellas) was a large number of independent city-states spread from Sicily to the Black Sea, sometimes grouped into mutual-defence leagues. There was a brief-lived Macedonian empire of Alexander the great (late 4th Century BCE), which on his death split into Hellenistic kingdoms ruled by dynasties established by his generals (Egypt, Syria, Macedon, etc) after his death. These lasted until progressively absorbed into the expanding Roman Empire in the 2nd and 1st Centuries BCE .