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

No

While the spelling and the fundamental meaning of "resposta" (answer/response) are identical in both Brazilian and Continental Portuguese, there are differences in typical usage (syntax) and pronunciation.

• Usage/Grammar: In Brazil, it is very common to use the preposition "para" after "resposta" (e.g., resposta para a pergunta). In Portugal, the preposition "a" is much more standard (e.g., resposta à pergunta).
• Pronunciation: Brazilian Portuguese tends to have more open, clear vowels. Continental Portuguese is characterized by "vowel reduction," where unstressed vowels are much more closed or even almost silent, giving the speech a more consonant-heavy sound.

Brazilian Portuguese Examples

1. Eu não sei a resposta para essa pergunta. (I don't know the answer to this question.)
2. Estou esperando a sua resposta por e-mail. (I am waiting for your reply via email.)
3. Ele deu uma resposta muito grossa. (He gave a very rude answer.)
4. Você já recebeu uma resposta do médico? (Have you already received an answer from the doctor?)
5. Essa é a resposta que eu precisava. (That is the answer I needed.)

Continental Portuguese Examples

1. Não sei a resposta a esta pergunta. (I don't know the answer to this question.)
2. Estou à espera da tua resposta por e-mail. (I am waiting for your reply via email.)
3. Ele deu uma resposta bastante grosseira. (He gave a very rude answer.)
4. Já tiveste uma resposta do médico? (Have you already received an answer from the doctor?)
5. Essa é a resposta de que eu precisava. (That is the answer that I needed.)