A republic is probably referring to Rome. Which became a republic around 500 b.c.
A satrap is a Persian governor that ruled over a region. They were implemented under Cyrus the great around 600 b.c.
The mandate of heaven is a Chinese belief regarding the dynasties. The Chinese believed that their gods chose the dynasties, and that when things went south for China the dynasty fell out of favor of the gods. This was around 1000 b.c.
Royal road is persians they built the road for trade and transport. This was a very ambitious building project for the time and was commanded under Darius the great. This was around 500 b.c.
Agustus was a Roman general/ emperor who ruled from 27 b.c to 14 ad. He was the first Emperor in Rome.
The Achaemendid Empire is considered the first Persian empire. It was founded by Cyrus the great in 550 b.c.
The Hellenistic era is a Greek era that significantly spread the Greek culture. The hellenistic Era started in 323 b.c, between the death of Alexander the Great and the start of the Roman empire.
Ashoka the great Ruled most of the Indian subcontinent. He ruled around 232 b.c.