Final answer:
The military commands during the time of the First Triumvirate were: Pompey in the Mediterranean and Eastern regions, Crassus in Syria against the Parthians, and Caesar in Gaul. Their conquests and political maneuvers significantly impacted the Roman Republic.
Step-by-step explanation:
Pompey had a command in the Mediterranean and Eastern regions, Crassus had a command in Syria against the Parthians, and Caesar had a special military command in Gaul. Pompey, known for his military prowess, was initially tasked with clearing the Mediterranean of pirates, later conquering territories like Judea and suppressing revolts in Anatolia. His achievements expanded the Roman Empire considerably. Crassus, on the other hand, was ambitious and sought military glory and riches but ultimately met his end during his campaign against the Parthians, where he was captured and executed. Julius Caesar, famed for his strategic genius and military strength, was appointed to lead Roman armies in Gaul where he achieved significant success, notably against the Celtic king Vercingetorix.
These pivotal roles played by the members of the First Triumvirate shaped the political and military landscapes of the Roman Republic during their time. Caesar's victories in Gaul made him immensely powerful and popular, which alarmed the Senate and eventually led to the desperate measures of calling upon Pompey to oppose Caesar's rise to power. The conflict between Caesar and Pompey escalated, with Caesar ultimately emerging victorious in the civil war that ensued.