Catalyzes the formation of isopentenyl diphosphate (IPP), the building block of all isoprenoids. Has no activity with farnesyl phosphate. ATP + isopentenyl phosphate = ADP + isopentenyl diphosphate Optimum pH is 7-9. Retains 38% activity when incubated at 100 degrees Celsius for 10 minutes. Homodimer. Belongs to the isopentenyl phosphate kinase family.