Is the word exato the same in Brazilian and European Portuguese?

Yes

The word "exato" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, vowels are typically more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo "vowel reduction," meaning they are shorter and more closed, which can make the word sound more clipped or subtle to a Brazilian ear.

Brazilian Portuguese Examples

1. Isso é exatamente o que eu queria. (That is exactly what I wanted.)
2. Qual é o horário exato do voo? (What is the exact time of the flight?)
3. — Você concorda? — Exato! (— Do you agree? — Exactly!)
4. Precisamos de uma resposta exata. (We need an exact answer.)
5. O lugar exato é aquele ali. (The exact place is that one over there.)

Continental Portuguese Examples

1. É precisamente o que eu queria. (It is precisely what I wanted.)
2. Qual é a hora exata do voo? (What is the exact hour of the flight?)
3. — Concordas? — Exato! (— Do you agree? — Exactly!)
4. Precisamos de uma resposta exata. (We need an exact answer.)
5. O sítio exato é aquele ali. (The exact place is that one over there.)