The word exploit has two distinct meanings:

1. To use something effectively or to your advantage. A basketball team might exploit their opponent's weakness in defending three-point shots. A chess player exploits an opening in her opponent's defense. When scientists discover a new material, engineers look for ways to exploit its properties, finding useful applications for it. This meaning carries no judgment: you can exploit an opportunity, exploit your strengths, or exploit a situation in completely fair and honest ways.
2. To treat someone unfairly by taking advantage of them. A company exploits its workers when it pays them poorly while making huge profits from their labor. A bully exploits a younger student's fear to make them do his homework. When someone is being exploited, they're being used in a way that benefits someone else while harming or cheating them. This meaning of exploit is always negative.

The difference matters: exploiting your talent for math is admirable, but exploiting your friend's generosity makes you a bad friend. Context tells you which meaning applies.

As a noun, an exploit means a bold or daring achievement, like the exploits of famous explorers.