Final answer:
The Ottoman Empire rose to prominence after the fall of Rome, reaching its height with the conquest of Constantinople by Sultan Mehmed II and becoming a major power in the 15th and 16th centuries.
Step-by-step explanation:
After the fall of Rome, the empire that quickly rose to prominence and established a substantial dominion was the Ottoman Empire. The Byzantine Empire, the eastern part of the former Roman Empire, continued until 1453 when Constantinople fell to Sultan Mehmed II, also known as Mehmed the Conqueror. This marked the beginning of Ottoman ascendancy, which at its peak encompassed large areas across the Middle East, North Africa, and Southeastern Europe, creating one of the most powerful empires in history during the 15th and 16th centuries.