Final answer:
The Mayan kings' power and authority came from their political and administrative control, leadership in warfare and infrastructure projects, and their connection to the divine force known as K'in.
Step-by-step explanation:
The Mayan kings' power and authority derived from multiple sources. They held political, administrative, and judicial control over their society. They were also responsible for leading the army in battles and carrying out large-scale infrastructure projects. However, their power was not solely based on secular authority. The Maya believed in a divine force called K'in, which was represented by the sun's energy. The kings were seen as conduits for this divine energy and were able to secure the allegiance of their subjects through their ability to predict natural events and seemingly control time.