Final answer:
The Maya, Aztec, and Inca rulers commanded ultimate power due to their roles as divine or semi-divine leaders of highly structured societies, managing political, religious, and societal duties, while engaging prominently in public works and exacting tribute.
Step-by-step explanation:
The Maya, Aztec, and Inca rulers had unquestionable power because they were at the apex of highly stratified societies and were seen as divine or semi-divine figures. They held authority over the political, administrative, and religious spheres, and were responsible for maintaining order and prosperity. Notably, these rulers engaged in public displays of power and commanded extensive infrastructure projects like the building of pyramids. This control was also exemplified in the way tribute was exacted, and the reliance of society on the rulers for provision of goods and services, as seen most clearly in the Inca Empire.
Furthermore, the nobility and priestly classes had significant influence, with only nobles having the luxury of certain privileges and monopolizing important roles in government and religion. For the Aztecs, each city-state was governed by a tlatoani who not only oversaw tribute collection and military campaigns but was also a representative of the gods.
In line with this, the Maya rulers, or 'divine lords', exercised their power through control over religious rituals, temple construction, and warfare with other city-states. The Maya, Aztec, and Inca cultures, with their permanent stone architecture and valuing of the arts, reflected the potency and sophistication of their rulers.