Catalyzes the decarboxylation of mevalonate 5-diphosphate (MVAPP) to isopentenyl diphosphate (IPP). Functions in the mevalonate (MVA) pathway leading to IPP, a key precursor for the biosynthesis of isoprenoid compounds such as archaeal membrane lipids. (R)-5-diphosphomevalonate + ATP = ADP + CO2 + isopentenyl diphosphate + phosphate Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via mevalonate pathway; isopentenyl diphosphate from (R)-mevalonate: step 3/3. Homodimer. Belongs to the diphosphomevalonate decarboxylase family.