Answer:
The United States came to power because it led the allied offense in Western Europe against Nazi Germany, and in the Pacific against Imperial Japan.
The war effort also lifted the U.S. out of the Great Depression, and helped the country develop its industry and military even more, at the time that its main competitors were trying to recover from the effects of the war (Germany, France, Britain, Italy, Japan).
The Soviet Union came to power in a similar manner. It led the allied offense against Nazi Germany in Eastern Europe, and it took control of the Eastern European countries. The war also helped the Soviets developed its military and industry, and they had scientific achievements that were on par with those of the United States.