The Spanish ultimately took control of the Inca and Aztec Empires for multiple reasons, but the most significant response would be: The Spanish took advantage of civil war.
In both empires, internal conflict weakened their ability to resist the Spanish conquest. For instance, the Aztecs were facing unrest and resentment among conquered peoples, while the Incas were embroiled in a civil war at the time of the Spanish arrival. Additionally, the Spanish did exploit their superior weaponry and the impact of diseases like smallpox, which devastated local populations, but civil strife was a crucial factor in their conquest.