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

Yes

The spelling, meaning, and grammatical function of "cuidadosamente" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. Brazilian Portuguese features more "open" vowels, where syllables are clearly articulated. In contrast, Continental Portuguese features "closed" or reduced vowels, where unstressed syllables are often shortened or almost swallowed, giving the word a more consonant-heavy and clipped sound.

Brazilian Portuguese Examples

1. Ele limpou os óculos cuidadosamente. (He cleaned the glasses carefully.)
2. Por favor, coloque os pratos cuidadosamente na mesa. (Please, place the plates carefully on the table.)
3. Ela leu o contrato cuidadosamente antes de assinar. (She read the contract carefully before signing.)
4. O bebê foi colocado cuidadosamente no berço. (The baby was placed carefully in the crib.)
5. Você precisa pensar cuidadosamente antes de tomar uma decisão. (You need to think carefully before making a decision.)

Continental Portuguese Examples

1. Ele limpou os óculos com cuidado. (He cleaned the glasses with care.)
2. Por favor, põe os pratos com cuidado na mesa. (Please, put the plates carefully on the table.)
3. Ela leu o contrato com atenção antes de assinar. (She read the contract with attention before signing.)
4. O bebé foi colocado com cuidado no berço. (The baby was placed with care in the crib.)
5. Tens de pensar com cuidado antes de decidires. (You need to think with care before deciding.)