Final answer:
The incorrectly matched term is the "republican government clause"; it should reference the guarantee of a republican form of government to each state, not shared power between states and the federal government.
Step-by-step explanation:
The term incorrectly matched with its definition is the "republican government clause" – the correct understanding of this term should reflect the idea that the United States is to guarantee each state a republican form of government, rather than implying that states and the federal government share power, which is more related to the concept of federalism outlined elsewhere in the Constitution.
The Supremacy Clause, as correctly defined, states that the Constitution is the highest law in the land, overtaking any state law that comes into conflict with it. The notion of implied powers reflects powers of the federal government that are not explicitly stated but are necessary to execute the enumerated powers, as established in the Necessary and Proper Clause. Lastly, the Full Faith and Credit Clause requires that states respect the public acts, records, and judicial proceedings of every other state.