Final answer:
The Aztec and Inca empires could not resist European powers due to technological inferiority, forced labor systems, and lack of immunity to diseases such as smallpox, which decimated their populations.
Step-by-step explanation:
The empires of the Aztec and the Inca were unable to effectively resist the takeover of European powers predominantly due to technological disparities, such as the Europeans' use of gunpowder, steel swords, and horses. Beyond the immediate military defeats, the impact of European arrival was catastrophic, with smallpox, typhus, and other diseases wiping out vast numbers of native inhabitants who had no immunity to these novel illnesses.
Population decline was accelerated by the harsh Encomienda system which led to brutal exploitation and further weakened the ability of indigenous populations to resist. Diseases brought by Europeans, like smallpox and measles, spread quickly among the native population, causing widespread mortality and disrupting societies on a massive scale. This biological devastation, coupled with exploitation, war, and forced labor, meant that native populations were facing severe challenges from multiple fronts, making effective resistance profoundly difficult.