Explanation:

- Gautamiputra Satakarni was a prominent ruler of the Satavahana Empire. The Satavahanas were an ancient Indian dynasty that ruled in the Deccan region.

- The Chera Empire was an ancient Tamil dynasty that ruled in present-day Kerala and parts of Tamil Nadu, not associated with Gautamiputra Satakarni.

- The Rashtrakuta Empire came into prominence much later, around the 8th to 10th century CE, in southern and central India.

- The Chola Empire was a significant power in Southern India, but its most famous rulers were from a much later period, the medieval era.

- Option 4 - Satavahana is the correct answer to describe the empire that Gautamiputra Satakarni ruled.