There are a few young German students at my university and when they speak in German I noticed they often say 'genau' or 'ja, genau' in response to a statement made by someone else. Is this something like 'Exactly' in response to a statement or 'Yeah, right'.
Yes, Genau! is just an affirmative response, which literally translates to exactly, meaning It is exactly as you said and could well be translated into Right!, Correct!.
That pretty much depends on tone of voice.
Genau, used in normal voice means "exactly". Almost just a filler with confirmatory intent. Factual agreement. That is probably the most often heard case, and the usually the only one that dictionaries tell you about.
So, I gather from this observation that the sun is at the center of our solar system? – Genau.
But genau used in a sarcastic/ironic/sardonic voice has to be translated differently. Often the last syllable is signalling hysterical content by being raised, more melodic than usual and/or somewhat stretched. Or like @Marv commented: "The second is also true when it‘s spoken something like ‚genauuu‘ (or „ge-nauuu“), meaning with a dragged out ‚u‘."
In that case it is more or of the "Yeah, right" or "can't be serious", or even "you're pulling my leg!", "nonsense". Then it is not "exactly", but the exact opposite!
So, I know since childhood that the moon is what we call the sun at night. – 'Ge-nau'