How did jefferson’s purchase of louisiana simultaneously contradict his theory of government and also support his idea of republicanism?

Jefferson supported limited government power and was anti-federalists. Therefore, his purchase of land was against his philosophy.

Explanation:

Jefferson's believed that as per the constitution, the president does not contain any power to purchase lands.   However, he purchased the land to increase the nation's power and expand his territory, which comes under the power of the governing authorities. On the other hand, some federalists were against this purchase as they claimed it was unconstitutional.

Therefore, Jefferson's action was both against his theory and in favor of republicanism.

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wait history, who want to talk about history, boring.