Why did the united states assert itself as a worlds power

Because of the economic compatibility and military prowess.
Also the US traded many things such as led (1.8 billion in the 1800's) this made it a world market.

The U.S assert  themselves as the world's power because of the economical and military strenght of the country. Because of the highly influential role in the world's politics, the president of USA is considered as the most powerful person in the world.