*Their chefs have been cooking them [safe/ safely] for centuries.
It says the answer of the questions is 'safely.'
But I don't see why we can't use 'safe.'
Can you give me any good explanation about this?
Bibliolept is correct, yet I can see a source of confusion here. Suppose a student taking the test thinks that cooking safe/safely refers to the item being cooked. Cooking safely
clearly should refer to the actions of the chefs, and not whatever they are cooking.
In idiomatic English, we wouldn't use this construction at all, but would say something like, The xxxxxx was made safe (to eat) by cooking.