Final answer:
During the Greek Classical period and the Roman Empire, the ancient Greeks and Romans were leading the way in culture, art, and philosophy.
Step-by-step explanation:
A time when the ancient Greeks and Romans were leading the way in culture, art, and the philosophies was during the Greek Classical period (900 to 480 BCE) and the Roman Empire. The Greeks during this time were undergoing a major change in their thinking and cultural achievements. They moved from an oral to a literate culture and from a foundation of religious belief and mythology to art and rational thought. The Romans, on the other hand, admired and adopted Greek culture, modeling their architecture on Greek buildings and studying Greek ideas.