Range hood - not powerful enough to clear smoke?
As many have mentioned the exhaust duct needs to be sized properly, I have seen folks spend a lot on higher cfm fans that did no better because the root problem was the home was sealed so no air could get in to efficiently allow the hood to do its job. Try opening a window and see if the hood works better. If no change the duct may be two small, if the hood works with the window open you have a cheap fix. More expensive methods involve pressure switches and make up air from outside.