Which word means impervious to external influences?

The term "impervious" directly denotes a state of being unaffected or resistant to external influences or conditions. When something is described as impervious, it implies that it cannot be penetrated or influenced by outside forces. This is consistent with the context of the question, as it seeks a word that conveys a lack of vulnerability to external factors.

In contrast, the other choices represent very different meanings. "Pliable" refers to something that is easily bendable or flexible, suggesting that it can be influenced or shaped. "Exhausted" indicates a state of extreme tiredness or depletion, which does not relate to external influence. Lastly, "permeable" describes a quality where something can be penetrated or passed through, meaning it is open to external influences rather than resistant to them. Therefore, "impervious" stands out as the correct term that encapsulates the meaning of being impervious to external influences.