Jefferson strengthened the power of the federal government by buying the Louisiana Purchase. This purchase lead to the United States getting 828 million square miles of territory which will eventually become part of 13 different US states west of the Mississippi River.
This strengthened the power of the federal government because there was no precedent (example) as to whether or not the president could buy land from a foreign country. Since the US Constitution had no specific law on this matter, Jefferson argued that this was an implied power, meaning even though it is not written down it could be implied that the president has this power.
From this point on, future presidents use this power to annex territories to make them part of the United States.
