Learn Italian: Ho avuto un imprevisto e non sono potuta venire. - I had an unexpected event and I couldn't come.

When a modal verb like potere (can / to be able to) is followed by an infinitive, it borrows the auxiliary verb that the infinitive uses. Because the infinitive here is venire (to come), which is a verb of motion that takes essere, the modal verb also takes essere.

Why does potere become potuta with an 'a' at the end instead of potuto?

Whenever you use essere as the helping verb in the past tense, the past participle must match the gender and number of the subject. In this sentence, the speaker is female, so she says potuta. A male speaker would say non sono potuto venire.

Why do we use avere for the first half (Ho avuto) but essere for the second half (sono potuta)?

These are two separate actions. The first action is simply the verb avere (to have), which always takes avere as its helping verb (ho avuto). The second action uses essere purely because of the rule connecting the modal verb to venire.

What exactly is un imprevisto?