'Brow' is used only in written English, with very few exceptions. Neither 'forehead' or 'brow' is considered slang. If I want to create an image in writing of somebody deep in thought or having some doubts, I would say that their brow was 'furrowed' (wrinkled).

Gary this is a question from my teacher. And I continue in doubt.

Agreed. Those terms, if anything, relate to styles, and rarely words. In this case, brow, being somewhat archaic, would be most often be used (a)literally, as in Frank's example, but also (b) in 'brow-beaten' - which is more colloquial. Adriana - is this a question from some book, or teacher?

The only phrase I hear used very often is "by the sweat of my brow" or a firm of that, sometimes used sarcastically.

I take issue with the idea of "register". You would write that I speak "literary English", but I also use that same form of English in my technical, scientific writing. I conduct business in that language and I taught it to my children. In my opinion there is standard English and substandard English. Trying to classify one as "colloquial" versus "slang" adds an unnecessary complication. It is similar to saying that one language is a "creole" while another is a "pidgin".