Final answer:
Suleiman the Magnificent, Akbar the Great, and Louis XIV shared a similarity in their approach to governance by embracing and promoting the dominant religious and cultural views, which included portraying themselves in a manner that upheld the power and prestige of their royal positions.
Step-by-step explanation:
One way in which Suleiman the Magnificent, Akbar the Great, and Louis XIV are similar is that each was a ruler who embraced the dominant religious and intellectual views of their subjects and portrayed themselves in ways that fitted the power and status that their royalty was perceived to hold within their respective cultures.
For instance, Suleiman the Magnificent of the Ottoman Empire was known for his patronage of arts and architecture and for the religious tolerance granted towards non-Muslim subjects. Akbar the Great of the Mughal Empire is renowned for his progressive outlook towards religious tolerance and even attempted to create a syncretic religion to unite his subjects. Louis XIV of France, also known as the Sun King, was a central figure of his kingdom, promoting the arts and embodying the absolute monarch.
These rulers adapted to their cultural contexts and embodied ideals that promoted the coherence and stability of their states through strategies of cultural and religious inclusion or syncretism while also projecting their majestic image as part of their royal authority and legitimacy.