Tending to exhibit, display, or show something; relating to or characteristic of exhibition.
From exhibit + -ive (adjective suffix meaning 'tending to' or 'relating to'). The suffix -ive is common in English for forming adjectives from verbs.
The word 'exhibitive' sounds like it should be more common than it is—the -ive suffix usually creates productive adjectives, but 'exhibitive' remains quite rare in everyday English.
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