People in the south used slaves because their economy was focussed on things like cash crops (tobacco, cotton, etc.) These crops required a lot of work so farmers and plantation owners could not do it by themselves. So by using enslave persons they could harvest more crops, sell more, make more money, and in return boost the southern economy.
Uh, I think you got the wrong subject. This is <em>History, </em>not Math.
None of them are really more powerful than any other they share the power and the all play a powerful role in our us government, to prevent any branch from becoming to powerful they would use a system called checks and balances.