Like the Romans used to drink from lead cups. Something like that.
(it appears that the moderator is removing any replies with which he disagrees. It might be a piefed issue. But all the removed replies are top level and upopular. Stranger coincidences have happened I suppose.)
Powered doesn’t mean the vent exits outside.
Vents that vent to the outside over gas hoods need to be required by law, otherwise, it may, or may not.
When I bought my house, I’d never seen a range vent that didn’t vent to the outside, so I didn’t know such things existed. I didn’t check, and mine doesn’t. It’d be at least $8K to have a hole cut in my roof for the vent to run to the outside.
$8k if you pay someone to do it. <$300 if you do it yourself. I’ve done it twice, once for bathroom exhaust and once for the stove