Final answer:
Julius Caesar was the strongest militarily in the First Triumvirate and he conquered Gaul. His military success was important for gaining political power and transitioning the Republic into an Empire.
Step-by-step explanation:
The member of the First Triumvirate who was the strongest militarily speaking was Julius Caesar. Caesar was appointed general of the territory of Gaul (present-day France and Belgium) and he successfully conquered all of Gaul. He also launched attacks against German tribes across the Rhine and on the island of Britain. Crassus, another member of the First Triumvirate, invaded the Parthian Kingdom in central Asia but his invasion was a disaster and he was captured and executed.
Caesar's military success was important because it solidified his popularity among the Roman people. His conquests in Gaul and his military reputation allowed him to gain political power and influence, which helped him eventually become the sole leader of Rome and transition the Republic into an Empire.