Learn Hardcore Portuguese (Brazil): A professora vai explicar o exercício de português depois da aula. - The female teacher will explain the Portuguese exercise after class.

Talking about someone’s profession (after ser):
- Ela é professora. = She is a teacher.
  Here you normally don’t use the article.
Talking about a specific person as the subject or object:
- A professora vai explicar… = The teacher is going to explain…
  You do use the article because you mean a specific, known teacher.

So:

Ela é professora. (She is a teacher – profession in general)
A professora vai explicar. (The teacher – that specific one – is going to explain)

What tense is vai explicar? Is it present or future?

Grammatically, vai is the present tense of the verb ir (to go), and explicar is an infinitive. Together, ir (present) + infinitive forms what’s often called the “near future” or periphrastic future:

vai explicar = is going to explain

So:

Form: present of ir
infinitive
Meaning: a future action, usually fairly certain or planned

It functions like English “is going to explain”, not like “goes explain”.

Can I say A professora explicará o exercício… instead of vai explicar?

Yes, but it sounds different.

A professora vai explicar o exercício…
– Very common, neutral, everyday future; used all the time in spoken Brazilian Portuguese.
A professora explicará o exercício…
– Simple (synthetic) future; sounds more formal, written, or “bookish” in Brazilian Portuguese. You do hear it, but less often in casual speech.

Meaning-wise, both are future, but vai explicar is what you’ll hear most in conversation.

Why is there o before exercício? Could I drop it?

o is the definite article “the”:

o exercício = the exercise

You use o here because both speaker and listener know which exercise is being talked about (for example, one on the board or in the book).

If you said:

A professora vai explicar um exercício… = The teacher is going to explain an exercise.

That would mean some exercise, not a specific one already known.

Usually, with a specific noun like this, Portuguese prefers to keep the article; dropping it (vai explicar exercício) would sound unnatural here.

In o exercício de português, what does de português mean exactly?

de português literally means “of Portuguese”, and it works like an adjective describing which exercise it is:

o exercício de português = the Portuguese exercise / the exercise from the Portuguese class / the exercise about Portuguese

This noun + de + noun structure is extremely common:

livro de matemática = math book
professor de inglês = English teacher
prova de história = history test

So de português is not “of a Portuguese person” here; it means the exercise is related to the Portuguese language/subject.

What’s the difference between de português and em português?

They express different ideas:

o exercício de português
= an exercise of the subject Portuguese (about grammar, vocabulary, etc.)
o exercício em português
= an exercise written in Portuguese (the language used is Portuguese)

Examples:

Vou fazer um exercício de português.
I’m going to do a Portuguese (language) exercise.
Posso responder em inglês ou tem que ser em português?
Can I answer in English or does it have to be in Portuguese?

In your sentence, de português is correct because it’s an exercise of the Portuguese class.

What does depois da aula literally mean, and why da?

Literally:

depois = after
de = of / from
a aula = the class / the lesson

In Portuguese, the expression is depois de + noun (“after of _”).
When de comes before the feminine article a, they contract into da:

de + a aula → da aula

So:

depois da aula = after (of) the class → “after class / after the lesson”

This contraction is mandatory in normal speech and writing; you don’t say depois de a aula.

Why is it da aula and not do aula?

Because aula is a feminine noun:

a aula = the class (feminine)
o would be for masculine nouns.

The contractions work like this:

de + a → da (feminine)
de + o → do (masculine)

Examples:

depois da aula = after the class (feminine)
depois do filme = after the movie (masculine)

Can I move depois da aula to another place in the sentence?

Yes. Time expressions are fairly flexible in Portuguese. All of these are possible:

A professora vai explicar o exercício de português depois da aula.
Depois da aula, a professora vai explicar o exercício de português.

Putting depois da aula at the beginning is also very natural, especially in writing or when you want to emphasize the time.

Placing it in the middle like:

A professora, depois da aula, vai explicar o exercício de português.

is also grammatically correct, but sounds a bit more formal/emphatic. The original word order is the most neutral.

What exactly does aula mean? Is it the same as “class”?

aula usually refers to a lesson / class session, not the group of students.

Common terms:

a aula = the class/lesson (one session or subject time)
a turma = the class as a group of students
a classe = sometimes used for the group of students; also used in other senses (“social class”)

So:

depois da aula = after the (class) period
A turma é muito barulhenta. = The class (group of students) is very noisy.

How do I pronounce the main words in this sentence?

Approximate Brazilian Portuguese pronunciation (stressed syllable in bold, English-like hints):

professora → pro-fe-SO-ra
(“pro-fe-SO-ra”; so like “so” in English, final ra very light)
vai → vai
(rhymes with English “vie”)
explicar → es-pli-CAR
(car like “car”, but with a harder, tapped/rolled r)
exercício → e-zer-SÍ-sio
(zi like “SEE”; the r is soft, like in “Brazilian”)
português → por-tu-GUÊS
(final syllable stressed; ês like “ace” but with a more closed “e”)
depois → de-POIS
(“de-POYS”, roughly)
aula → AU-la
(au like “ow” in “cow”, then “la”)

These are approximate; real pronunciation varies by region, but this will be understood anywhere in Brazil.