Final answer:
Japan overcame the challenge of western imperialistic nations by embracing western technology and government, building their own empire, and becoming a world power.
Step-by-step explanation:
During the late 19th and early 20th century, Japan overcame the challenge of western imperialistic nations by embracing western technology and government while also building their own empire. They modernized their military and industry, sent scholars abroad to learn from the United States and Western Europe, and brought in Western advisers to guide their development. They also successfully defeated both Russia and China in wars, expanded their territory, and became a world power. By doing so, Japan was able to compete with larger countries and secure its position in the East.