The city of Machu Picchu from the Inca, the script of the Maya, and Tenochtitlan of the Aztec all demonstrate advanced abilities of these states, despite having few of the technologies associated with European counterparts at this time. In terms of Machu Picchu, its construction is an example of great knowledge for architecture and science. If the Inca did not have such a keen grasp of building and math, the city would likely slide off the cliff it was built on. When building, all calculations must be precise or it could ruin the integrity of the structure. Only precise measurements would capture water from the river nearby and supply the city with fresh water, even to this very day. There was no mortar in the walls, so each stone had to be matched perfectly. Not only did math and architecture allow the Inca to survive in a place that was visible throughout the surrounding valley, but it also let them display their skill and ability to control and manipulate resources.
The Mayan script allowed them to denote anything that was deemed important. It was a way to preserve their cultural traditions and create social stratification. Education became a commodity, left only to the elites. All of these calculations and records allowed them to have a firm control over the ranks of citizens.
Tenochtitlan was of supreme importance. First, it was a capital city based on an island. This means that the population base was able to adapt to living with the waters and still have enough influence and power to start appropriating resources into the temples. The temples and pyramids created visible markers of the reach of the Aztec. These also supported important ritual moments that would have strong political impacts. What better to impose a sense of awe and fear in your own population than to create a monumental structure that towers into the sky?
All three things display each state’s ability to create the image of a strong empire. They are technologically advanced and calculated monuments or decorations of monuments that promoted social stratification, elite power through control of resources, and added political clout to a rulers reign.