What was the primary power given to the lower house or assembly in colonial legislatures?

The primary power given to the lower house or assembly in colonial legislatures was to approve new taxes. This empowerment was significant because it established the principle of "no taxation without representation," whereby the assembly acted as the voice of the colonists. They had the authority to debate, modify, and ultimately decide on taxation policies, which allowed them to have a measure of control over the colonial budget and spending.

This power was critical in the context of colonial governance, as it laid the foundation for conflict with the British Parliament over taxation and representation. The assemblies could influence colonial economies and priorities through their control over taxation, asserting their importance in local governance in a way that shaped the relationship between the colonies and the British government. This role was pivotal as the colonies approached major historical events leading to the American Revolution.