She (study)______ architecture at university for the last three years

The correct form to fill in the blank is "has been studying."

The reason for this choice is that the sentence refers to an action that started in the past and continues into the present. The use of the present perfect continuous tense ("has been studying") indicates that she began studying architecture three years ago and is still studying it now.

In this case:
- "has" is the auxiliary verb for the subject "she" in the present perfect.
- "been" is the past participle of "be," which is used in continuous tenses.
- "studying" is the present participle of the verb "study."

Putting it all together, the complete sentence reads: "She has been studying architecture at university for the last three years." This structure effectively communicates the ongoing nature of her studies and emphasizes the duration of time she has spent on her education in architecture.