Final answer:
Indian alliances played a crucial role in European imperial power dynamics in the southeastern United States, and the Northern Plains drums are typically larger than Southern Plains drums. While diseases were a major cause for native casualties during exploration, the Louisiana Purchase significantly expanded the US territory.
Step-by-step explanation:
The Indian alliances were indeed a strategic aspect of establishing power in the southeast for European empires. Such alliances allowed European powers to leverage local conflicts and politics to gain an advantage over rival European nations and to secure important trade relationships, particularly in the lucrative fur trade. Establishing alliances with Indian tribes also facilitated the Europeans' territorial expansion by pitting different tribes against one another.
Regarding the drums, it's believed that Northern Plains drums are traditionally larger compared to those of the Southern Plains — an assertion based on cultural practices observed among the tribes. However, the cultural variations are intricate, and this can be seen as a general statement rather than an absolute one.
The majority of native populations during the era of exploration did not necessarily die from outright slaughter by European conquistadors. Many natives died from diseases that Europeans brought to the Americas, to which indigenous peoples had no natural immunity, such as smallpox, measles, and influenza.
Finally, the Louisiana Purchase did indeed double the territory of the United States, adding approximately 828,000 square miles of land west of the Mississippi River to the nation's domain and dramatically shaping the country's expansion.