Do we say
I've been to the hairdressers'
is the ' in hairdressers correct please?
If there is more than one hairdresser, then it is OK to say hairdressers', if there is only one hairdresser, then it is hairdresser's. The use of the apostrophe indicates that there is a word missing, "the hairdresser's [shop, salon, etc.]. It is also common (and universally acceptable) to omit the apostrophe, "I've been to the hairdresser (or hairdressers if you've seen more than one)."
All of the forms, singular, plural and their possessives are correct, they just have slightly different meanings.