The most accurate response regarding the investigation of the Aztec and Inca Empires in the context of their encounters with the Spanish would be:
their armies were too small to defeat the Spanish.
While there were multiple factors contributing to the downfall of both empires, including internal strife, disease, and the technological advantages of the Spanish, one significant factor was the relatively smaller size of their armies compared to the forces they faced and the strategic advantages that the Spanish possessed.