How might new innovations have enabled european countries to dominate other to countries or regions ?

The Industrial Revolution in Great Britain in the middle of the 18th century marked the beginning of a technological gap that would define the political landscape of the world in favor of the European nations. This period supposed the creation of many devices that improved not only these regions economical activities but also the military, as European navies were able to settle in many parts throughout the world with relative ease. Improvements in weaponry gave Europans the edge when it came to conflicts with locals in different parts of the world.

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

you didn't give any answers to choose from so i can't with this but, i do know something that the mexican government would be worried about and that is the wall that donald trump is currently trying to get up.