Final answer:
State governments are delegated the authority to regulate intrastate trade, which is commerce that occurs within a state's own borders. This is part of the reserved powers under the federal system.
Step-by-step explanation:
The question pertains to the division of powers between the federal and state governments in the United States. Among the four options provided, the authority specifically delegated to state governments is to regulate intrastate trade. States have reserved powers which involve the regulation of commerce within their own borders, along with conducting elections, maintaining state militias such as the National Guard, regulating education through establishing public schools, and more. These reserved powers are part of the federal system to ensure a balance between national and state functions.