The powers granted and denied to the states and the federal government are outlined in the US Constitution. Here are some examples:
Powers granted to the Federal Government:
Regulating interstate commerce
Declaring war
Creating and maintaining the armed forces
Printing money
Conducting foreign relations
Establishing a postal system
Powers denied to the Federal Government:
Prohibiting freedom of speech, religion, press, or assembly
Prohibiting the right to bear arms
Prohibiting trial by jury
Prohibiting habeas corpus (the right to a fair trial)
Passing ex post facto laws (laws that punish someone for an action that was legal when they did it)
Granting titles of nobility
Powers granted to the States:
Regulating trade within the state
Establishing local governments
Conducting elections
Providing public education
Regulating marriage and divorce
Regulating intrastate commerce
Powers denied to the States:
Printing money
Declaring war
Conducting foreign relations
Prohibiting freedom of speech, religion, press, or assembly
Prohibiting the right to bear arms
Prohibiting trial by jury
It is important to note that the powers of the federal government are generally broader than those of the states. However, the Tenth Amendment to the Constitution reserves all powers not specifically granted to the federal government to the states or to the people. This means that the states have some degree of flexibility in how they govern themselves and can create their own laws and policies within the boundaries of the Constitution.