Final answer:
America asserted itself as a world power through economic strength, territorial expansion, and military influence during the imperialist age.
Step-by-step explanation:
America asserted itself as a world power during the imperialist age through a combination of economic strength, territorial expansion, and military influence. Firstly, the United States rapidly became a major manufacturing power and source of exports, which created fear and competition among European nations. Secondly, the US acquired territories such as the Philippines, Guam, and Hawaii, expanding its political and economic control. Lastly, the US utilized its military power and influence to protect its interests and assert dominance in the international arena.