Madurai became a prominent center of power under the rule of:

Vijayanagara Empire
Madurai Nayaks
Cholas
Pandyas

The correct answer is: b) Madurai Nayaks.

The Madurai Nayaks were a Telugu dynasty that ruled the Madurai region of southern India from the 16th to the 18th centuries. They were originally feudatories of the Vijayanagara Empire, but they became independent after the fall of the empire in the 16th century. The Nayaks were patrons of art and architecture, and they built many temples and palaces in Madurai. They were also known for their military prowess, and they fought off several invasions from the Mughal Empire.

The Vijayanagara Empire was a Hindu empire that ruled over much of southern India from the 14th to the 16th centuries. The empire was founded by Harihara I and Bukka Raya I, two brothers who were generals in the Hoysala army. The Vijayanagara Empire reached its peak under the rule of Krishnadevaraya, who reigned from 1509 to 1529. Krishnadevaraya was a great military leader and a patron of the arts. He expanded the empire to its greatest extent and built many temples and palaces. The Vijayanagara Empire declined in the 16th century due to a number of factors, including internal conflicts and invasions from the Mughal Empire.

The Cholas were a Tamil dynasty that ruled over much of southern India from the 9th to the 13th centuries. The Cholas were a powerful military and naval power, and they extended their empire to include parts of Sri Lanka, Southeast Asia, and the Maldives. The Cholas were also patrons of the arts and architecture, and they built many temples and palaces. The Chola dynasty declined in the 13th century due to a number of factors, including internal conflicts and invasions from the Pandyas.

The Pandyas were a Tamil dynasty that ruled over much of southern India from the 6th to the 13th centuries. The Pandyas were a powerful military and naval power, and they extended their empire to include parts of Sri Lanka, Southeast Asia, and the Maldives. The Pandyas were also patrons of the arts and architecture, and they built many temples and palaces. The Pandya dynasty declined in the 13th century due to a number of factors, including internal conflicts and invasions from the Cholas.