Some fighting for influence did take place between the two superpowers. Where?

The Cold War was an ongoing political rivalry between the United States and the Soviet Union and their respective allies that developed after World War II. This hostility between the two superpowers was first given its name by George Orwell in an article published in 1945.

Explanation:

president thomas jefferson commissioned the expedition shortly after the louisiana purchase in 1803 to explore and to map the newly acquired territory, to find a practical route across the western half of the continent, and to establish an american presence in this territory before britain and other european powers