Could someone explain the nuances between the two?
- 答え: (correct) answer, answer to a problem/question
- 受け答え: verbal response, (conversational) exchange
答え is what's important in an examination, and is synonymous to 解答, 回答 or 正答. 受け答え is what's important in an interview, and is synonymous to 応答 or やりとり. 答え is what you "give", whereas 受け答え is what you "do".
答え is an answer to a question which is correct, or expected to be correct, like answers on this site. 受け答え is about responding appropriately and smoothly in a conversation. It includes answering questions, but is not limited to that. For example, responding to a joke or even using proper keigo is part of 受け答え.