Relating to or intended for the purpose of exterminating; serving to destroy completely.
From exterminate + -ory (Latin -orius, a variant of -ive). Both -ative and -ory suffixes are related and mean 'serving to' or 'tending to.'
You're more likely to hear 'exterminatory' in formal or legal contexts—like environmental regulations forbidding 'exterminatory practices' in wildlife management—whereas 'exterminative' sounds more literary.
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