The Collaborative International Dictionary of English v.0.48:
Inexterminable \In`ex*ter"mi*na*ble\, a. [L. inexterminabilis. See In- not, and Exterminate.] Incapable of extermination. --Rush. [1913 Webster]WordNet (r) 3.0 (2006):
inexterminable adj 1: incapable of extermination or extirpation; "some weeds seem inextirpable" [syn: inexterminable, inextirpable]