Do you mean expressed powers and implied powers? Expressed powers are explicit in the Constitution meaning that they are written down in the section outlining the powers of Congress, the President and the Judicial Branch. Implied powers are powers that are implied in the Constitution. For example, the Constitution makes no mention of regulating radio waves (since there was no radio when the Constitution was written) but since they have the power to regulate commerce between states, if you consider radio waves going over state lines, then they also have the power to regulate radio waves. Also, radio is a business so it is commerce. This helps our Constitution be flexible and still used today.
powers listed in the Constitution
Concurrent Powers
Implied powers are congress exercised powers which are not given explicitly by the constitution. While express powers are the powers which is given by the constitution.
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There really is no difference between popular sovereignty and separation of powers. The only difference is that popular sovereignty falls under the separation of powers. With the latter, powers are allocated to local, state, regional, national, and federal authorities. Popular sovereignty is a state power, which allows states to pass certain laws and amendments based on their specific needs.
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Seperation of powers