Translation:We have to end this exploitation.
We need to end this exploration. - "Nós precisamos acabar com esta exploração."
If I was going from English to Portuguese, I probably wouldn't have known to put the "com" after acabar. Can we use terminar instead of acabar here? If so, do we still need to use "com" after that?
The best is "eu terminei meu dever de casa", as you proposed.
"Acabar and Terminar com" are more like putting a definitive end to some annoying thing.
So, in the case of "acabar com essa exploração", using "com" is better, as people are probably getting very upset with the exploitation and want to "put an end" to that.
In fights/competitions, "acabar com alguém" can mean "destroy/overwhelm somebody (the opponent)".
In relationships, "terminar com alguém" mean to end the relationship with somebody.
In general, literally, "acabar com algo" and "terminar com algo" can mean "to end up with something".