Final answer:
The Aztec Empire's fall to the Spanish was due to Montezuma's misconceptions, Cortés's military and political strategies, technological advantages, the impact of disease, and the Spaniards' alliances with other native tribes.
Step-by-step explanation:
The Aztec Empire fell to the Spanish conquerors for a variety of reasons. Notably, the Aztec people and their emperor Montezuma were deceived by Hernán Cortés partly due to Montezuma's belief that Cortés was a prophesied god, Quetzalcoatl, and thus initially welcomed him warmly. Military technology, such as steel armor and swords, also gave the Spanish an advantage over the Aztec's traditional weaponry. Allies with previously conquered tribes like the Totonacs, coupled with the devastating impact of smallpox, further weakened the Aztec resistance.
Cortés's manipulation of religion also played a role when he purified the temples, a symbolic act that replaced Aztec idols with Christian symbols, suggesting a willingness of the Aztecs to accept the new religion and authority. These factors, along with Cortés's calculated political alliances and military strategies, led to the capture of Tenochtitlán. The Spanish conquest was marked by Cortés's audacious hostage-taking of Emperor Montezuma, exploitation of civil unrest within the empire, and the eventual siege and defeat of Tenochtitlán, after which Cortés claimed the city, renaming it Mexico City.