What do you do with a smart mouth teen with bad attitude?

I have a 16 year old daughter she does very well in school.

But she does not do well at home with her younger brothers.

She is very rude and disrespectful to them and will say mean things like i hate you call them foul names and so on.

She does this in front of me all the time like im not even there she does get in trouble but it keeps happening .

she wont treat her friends this way and now its starting to rub off on her brothers.

what can i do to make her understand that they look to her as being the oldest?