The most accurate statement regarding how the search for maritime trade routes to Asia affected the growth of European empires is:
Several European nations began building overseas empires so they could access valuable trade goods such as spices.
This search for new trade routes was a significant driver for exploration during the Age of Discovery (15th to 17th centuries). European nations, motivated by the lucrative trade in spices, silks, and other commodities from Asia, embarked on voyages that ultimately led to the establishment of colonies and vast empires. Notable examples include the Portuguese and Spanish Empires, followed by the English, Dutch, and French, all of which expanded their territories and influence across Africa, the Americas, and Asia to secure access to these valuable resources. Thus, the quest for direct trade routes to Asia played a crucial role in the rise and expansion of European empires.