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

Yes

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

• Brazilian Portuguese: The vowels are more "open" and clearly articulated. The "e" and "i" sounds are pronounced distinctly.
• Continental Portuguese: There is a significant degree of vowel reduction. Unstressed vowels are often shortened or neutralized (for example, the "e" in "exer-" and the "i" in "-cios" are much more subtle, almost silent).

Brazilian Portuguese Examples

1. Eu preciso fazer meus exercícios de matemática. (I need to do my math exercises.)
2. Ele faz exercícios físicos na academia. (He does physical exercises at the gym.)
3. Os exercícios de respiração ajudam a relaxar. (Breathing exercises help to relax.)
4. Faça os exercícios da lição de casa hoje. (Do the homework exercises today.)
5. Eu terminei todos os exercícios da prova. (I finished all the exam exercises.)

Continental Portuguese Examples

1. Eu tenho de fazer os meus exercícios de matemática. (I have to do my math exercises.)
2. Ele faz exercício físico todos os dias. (He does physical exercise every day.)
3. Os exercícios de respiração ajudam a relaxar. (Breathing exercises help to relax.)
4. Faz os exercícios do trabalho de casa hoje. (Do the homework exercises today.)
5. Concluí todos os exercícios do exame. (I completed all the exam exercises.)