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Different Powers held by the U.S. Government

Delegated/Enumerated Powers

These are powers in the Constitution given to the national government. 

Examples

Power to lay and collect taxes
Power to regulate commerce
Power to establish post offices
Power to establish a rule of naturalization
Power to create courts inferior to the Supreme Court
Power to declare war
Power to raise an army and Navy
Power to make laws which are necessary and proper (Necessary and proper clause)

Concurrent Powers

Powers given to both the national government and the states.

Examples

Power to tax
Power to build roads
Power to establish bankruptcy laws
Power to create lower courts

Reserved Powers

This stems from the 10th amendment, which says "The powers not delegated to the US by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."

Examples

Power to regulate trade within the state
Power to conduct elections
Power to establish local governments
Power to establish public school systems

Implied Powers

Powers not listed in the Constitution that stem from the aforementioned Necessary and Proper Clause.  

Examples

Examples include creating a national bank, or regulating highways.

David Witten

States' Obligations to Each Other

Shortcomings of the Articles of Confederation