How does the statue of Prima Porta Augustus convey leadership and military prowess?
This is a great question. Let me first offer some historical context and then go over what the image shows.
The statute of Augustus is a little over six feet and it was discovered in 1863. It is now in the Vatican Museums. However, this statue is thought to be a copy of an original, which dates to the reign of Tiberius. Scholars believe that the original was given by Tiberius to his mother Livia and that the original was made of bronze.
The statue at is stands is a image of Augustus as emperor. More specifically, he is in the position of the chief military leader of Rome. He is wearing a thorax (breastplate). He also carries in his left hand a baton of consular power and with his right arm (raised), he is addressing the troops, presumably after victory.
Augustus is idealized and many scholars say that the sculptor got his inspiration from a statue from the sculptor Polykleitos (the statue of the Spear Bearer).
The facial expression is also one of seriousness, which fits a military general. Moreover, there is a slightly pensive look, as if Augustus is filled with further military conquests in mind.