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

Yes

The word "exercício" is identical in spelling, grammar, and meaning in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the pronunciation is more "syllable-timed," with more open and clearly articulated vowels. In Continental Portuguese, the pronunciation is "stress-timed," meaning unstressed vowels are often reduced, closed, or nearly swallowed, making the word sound more consonant-heavy and clipped.

Brazilian Portuguese Examples

1. Eu faço exercício na academia todos os dias. (I exercise at the gym every day.)
2. Este exercício de matemática é muito difícil. (This math exercise is very difficult.)
3. Você precisa fazer mais exercício físico. (You need to do more physical exercise.)
4. O professor passou um exercício para a turma. (The teacher assigned an exercise to the class.)
5. Fazer exercícios de respiração ajuda a relaxar. (Doing breathing exercises helps to relax.)

Portuguese (Portugal) Examples

1. Eu treino no ginásio todos os dias. (I train at the gym every day.)
2. Este exercício de matemática é muito difícil. (This math exercise is very difficult.)
3. Tu precisas de fazer mais exercício físico. (You need to do more physical exercise.)
4. O professor deu um exercício para a turma. (The teacher gave an exercise to the class.)
5. Fazer exercícios de respiração ajuda a relaxar. (Doing breathing exercises helps to relax.)