At the dawn of the Classical Era, the Persian Empire was the most dominant empire on earth. To this day, (as a % of earth's population) the Persian Empire was the largest in history. The Persian Empires emerged in Southwest Asia (Middle East).
The AP expects you to know ALL THREE:
- ACHAEMENID (550-330 BCE)
- PARTHIAN (247 BCE-224 CE)
- SASSANID (224-651 CE)
Just because the AP asks you to know all three Persian Empires... don't worry. When it comes to the Classical Empires, the Persian is not one of the "Major" empires (those would be Rome, Guptan India, and Han China). That being said, here is the key information on the Persian Empires.