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i think he meant colonial economies?
he/she asked: How did slaves help the colonies
I think it is the same everywhere when it comes to use of slaves as manpower. Think if we would have gotten the pyramids, the great wall and other man-made "wonders" without forced labor of the "slaves"
Slaves during the colonies helped the economy really good. They mostly worked in plantations and helped on growing crops. They worked on huge fields and back then, plantations and agriculture were important and farmers were the rich. If u weren't a farmer or own a property you're considered poor.
they bring about productions without a huge burden or minimized cost on behalf of the beneficiaries, which in the case of your question are the colonies. Economically speaking, all things considered (without constraint from lack of natural resources) profits increase as cost decrease and vice-versa. Just by this, we can already make a prediction that the colonies will be sitting on a huge profit for a very little cost, which can be considered the return on investment, ROI, - the purchase of the slaves in the trade.
I am too lazy to provide you the resources except on what I can remember on top of my head. But as a researcher or a student, you want to double check the validity of the information we provide you. :)