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

Yes

The word "exatamente" is identical in spelling, meaning, and grammatical function in both Brazilian and Continental Portuguese. The only differences lie in pronunciation:

• Brazilian Portuguese (BP): In many Brazilian dialects, the "t" followed by an "e" or "i" undergoes palatalization, sounding like the "ch" in "cheese" (e.g., exatach-mente). Vowels are generally more open and the rhythm is more melodic.
• Continental Portuguese (EP): The "t" remains a dental consonant (the tongue touches the teeth). Vowels are more closed, and unstressed syllables are often reduced or "swallowed," giving the word a more clipped, staccato sound.

Brazilian Portuguese Examples

1. Exatamente o que eu queria dizer. (Exactly what I wanted to say.)
2. Isso é exatamente o que aconteceu. (That is exactly what happened.)
3. O trem chega exatamente às oito horas. (The train arrives exactly at eight o'clock.)
4. Você entendeu exatamente o ponto principal. (You understood exactly the main point.)
5. É exatamente disso que eu preciso. (It is exactly this that I need.)

Continental Portuguese Examples

1. É exatamente o que eu estava a dizer. (It is exactly what I was saying.)
2. Isso é exatamente o que aconteceu. (That is exactly what happened.)
3. O comboio chega exatamente às oito horas. (The train arrives exactly at eight o'clock.)
4. Tu percebeste exatamente o ponto principal. (You understood exactly the main point.)
5. É exatamente disso que eu necessito. (It is exactly this that I need.)