Regarding authority, yes. A U.S. State Government (such as the State of Texas) administers the State in which is located. By contrast, the Federal Government of the United States of America administers the whole country.
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The state governments were much stronger. After their experience with Britain's king, the founding fathers gave very little power to the national government in fear of tyranny. Only after the failures of the Articles of Confederation was a strong national government seen as necessary.
Areas within a country have more power to rule themselves than in a different form of government.
It is good for the federal government to have special powers in order to uphold the constitution. If there was no central government, some state governments would treat citizens unfairly.
the relationship between the federal government and state governments is specifically laid out in the constitution
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they thought that state government should be more powerful than national gov.