Use the adjective hegemonic for the kind of authority and influence a powerful country has over a less powerful one. The U.S. is viewed as playing a hegemonic role in many parts of the world.
This word is common in politics, but you can also use it in cultural contexts when an imbalance of power is used to influence or control people. Forcing non-native speakers to speak only in English can be hegemonic — especially because in the U.S. and elsewhere, it's the dominant language. And at school the cool kids may have a hegemonic influence that compels everyone else to wear a certain brand of sneakers. Hegemonic has a Greek root, hēgemon, "authority."
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