The popularity of a burger or blue jeans, has a lot to do with the powerful influence of the American way of life. It means:

The culture of the politically and economically dominant society leaves its imprint on a less powerful society.

The correct answer is Option (1) → The culture of the politically and economically dominant society leaves its imprint on a less powerful society.

This phenomenon is a core concept of cultural hegemony, where a dominant culture (in this case, American culture) is spread through economic and political power. The spread of American products and cultural norms, such as fast food and clothing styles, is often linked to the United States' status as a superpower.