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

Yes

The word "exercitar" is identical in spelling, grammar, and meaning in both Brazilian and Continental Portuguese. The only differences are in pronunciation. In Brazilian Portuguese, the vowels are more open and clearly articulated. In Continental Portuguese, unstressed vowels (such as the first 'e' in exercitar) are often much more closed or even reduced to a near-silent sound, making the word sound shorter and more "clipped" to a Brazilian ear.

Brazilian Examples

1. Preciso exercitar minha mente lendo mais. (I need to exercise my mind by reading more.)
2. Este treino vai exercitar muito os seus músculos. (This workout will heavily exercise your muscles.)
   3. É bom exercitar o inglês todos os dias. (It is good to exercise/practice English every day.)
3. Você precisa exercitar sua paciência com as crianças. (You need to exercise your patience with children.)
4. Ele gosta de exercitar a criatividade no trabalho. (He likes to exercise creativity at work.)

Portuguese Examples

1. É preciso exercitar o cérebro. (It is necessary to exercise the brain.)
2. Vou fazer ginástica para trabalhar as pernas. (I am going to do gymnastics/exercise to work the legs.)
3. É importante praticar o inglês. (It is important to practice English.)
4. Temos de ter paciência. (We have to have patience.)
5. Ele gosta de usar a criatividade no trabalho. (He likes to use creativity at work.)