During the age of Imperialism what is happening with the U. S.'s political influence?

Power/ "American Empire"

Explanation:

"American imperialism is partly rooted in American exceptionalism, the idea that the United States is different from other countries due to its specific world mission to spread liberty and democracy. This theory often is traced back to the words of 1800s French observer Alexis de Tocqueville, who concluded that the United States was a unique nation, “proceeding along a path to which no limit can be perceived.”"

"“American imperialism” is a term that refers to the economic, military, and cultural influence of the United States on other countries. First popularized during the presidency of James K. Polk, the concept of an “American Empire” was made a reality throughout the latter half of the 1800s. During this time, industrialization caused American businessmen to seek new international markets in which to sell their goods. In addition, the increasing influence of social Darwinism led to the belief that the United States was inherently responsible for bringing concepts such as industry, democracy, and Christianity to less developed “savage” societies. The combination of these attitudes and other factors led the United States toward imperialism."

"Whatever its origins, American imperialism experienced its pinnacle from the late 1800s through the years following World War II. During this “Age of Imperialism,” the United States exerted political, social, and economic control over countries such as the Philippines, Cuba, Germany, Austria, Korea, and Japan. One of the most notable examples of American imperialism in this age was the annexation of Hawaii in 1898, which allowed the United States to gain possession and control of all ports, buildings, harbors, military equipment, and public property that had formally belonged to the Government of the Hawaiian Islands. On January 17, 1893, the last monarch of the Kingdom of Hawaii, Queen Liliuokalani, was deposed in a coup d’état led largely by American citizens who were opposed to Liliuokalani’s attempt to establish a new Constitution. This action eventually resulted in Hawaii’s becoming America’s 50th state in 1959."

source: https://courses.lumenlearning.com/boundless-ushistory/chapter/american-imperialism/

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the california missions began in the late 18th century as an effort to convert native americans to catholicism and expand european territory. there were 21 missions in all, lasting from 1769 until about 1833.   the missions were built by the spanish starting in 1769 in order to “colonize” the territory of alta california. so the missions were important because they were the means of settling california. it also wanted to keep other european countries out of alta california. building settlements along the coast would them meet these goals. missionaries wanted to convert the indians to the roman catholic faith. california indians did much of the work to build missions.