Final answer:
Nubian King Taharqo demonstrated his royal authority in Egypt by becoming culturally Egyptianized, supporting Egyptian religious traditions, and engaging in architectural projects, stressing continuity with past Egyptian rulers.
Step-by-step explanation:
The Nubian King Taharqo, a ruler of Egypt during the Twenty-fifth Dynasty, emphasized his royal power through several measures that mirrored traditional Egyptian practices.
By adopting Egyptian religious and cultural traditions, such as wearing the double crown, promoting the worship of Egyptian deities, and building temples in the Egyptian style, Taharqo strengthened his legitimacy as the pharaoh of Egypt.
He also strategically ruled from Memphis, supported the installment of Kusite princesses into significant religious offices like the 'God's Wife of Amun', and led a revival in art, architecture, and religious learning to maintain stability in Egypt.