Final answer:
Mayan city-states became more powerful through their dominance in warfare, control over trade routes, exacting tribute, and advancements in various fields.
Step-by-step explanation:
The relative power of Mayan city-states was influenced by their control over religious rituals, territorial expansion through warfare, and the ability to demand tribute from subordinate regions. Certain cities, like Tikal and Calakmul, grew more powerful due to victories in wars, which not only served a ritual purpose but also enabled them to subjugate other city-states and extract resources and labor.
Moreover, control over key trade routes and resources, such as cacao and maize, as well as luxury items like gold and turquoise, played a crucial role in the rise of powerful city-states. The advancement of the Maya in areas like mathematics, astronomy, and architecture, alongside their complex society, underscored the civility and sophistication of their culture.