Final answer:
The Spanish conquest of the Aztec Empire was facilitated by their superior military technology, alliances with rival indigenous tribes, and the introduction of smallpox, which devastated the Aztec population.
Step-by-step explanation:
The Spanish took advantage of several weaknesses in the Aztec Empire when they invaded Mexico.
Firstly, the military tactics and weaponry of the Spanish, such as steel armor and swords, and the use of horses, gave them a significant advantage over the Aztecs' bows and arrows and spears.
Secondly, the Spanish exploited political tensions by allying with indigenous tribes like the Totonacs and especially the Tlaxcalans, who were rivals of the Aztecs and provided substantial military support.
Lastly, the inadvertent introduction of smallpox by the Spanish had devastating effects on the native population, significantly weakening the Aztec society and its military capabilities.