"Develop" means to progress, grow or move something forward. Usually it has the connotations of being a gradual process where something is slowly improved or built upon over time.
e.x., We need to develop a plan for learning English.
"Exploit" means to take advantage of, or to utilize a weakness in something to get an advantage. It usually has slightly negative connotations as it tends to indicate you're using a flaw or a weakness to get an unfair advantage in something. It's not always negative though.
e.x., I exploited a bug in the program to beat the game.
You can exploit iTalki by asking native speakers to do your English homework.
Hope that helps!