Which political compromise sought to balance the power between free and slave states?

The Missouri Compromise is correct because it was specifically designed to maintain a balance between free and slave states as the country expanded westward. Enacted in 1820, this compromise allowed Missouri to enter the Union as a slave state while pairing its admission with Maine, which entered as a free state. This preserved the balance of power in Congress between the North and the South at that time. Additionally, the compromise established a line (the latitude of 36°30′) across the remainder of the Louisiana Territory, north of which slavery was prohibited. This arrangement was significant as it sought to address the contentious issue of slavery in new territories, foreshadowing the ongoing debates that would continue to escalate tensions leading up to the Civil War.

The other choices, while related to the complex issues surrounding slavery and statehood, served different purposes or occurred in different contexts, and did not combine the balance of power between free and slave states in the same direct manner as the Missouri Compromise did.