The Advanced Molybdenum-based Rare process Experiment in its second phase (AMoRE-II) will search for neutrinoless double-beta (0νββ) decay of 100 Mo in 200 kg of molybdate crystals. To achieve the zero-background level in the energy range of the double-beta decay Q-value of 100 Mo, the radioactive contamination levels in AMoRE crystals should be low. 100Enr MoO3 powder, which is enriched in the 100 Mo isotope, is used to grow the AMoRE crystals. A shielded array of fourteen highpurity germanium detectors with 70% relative efficiency each was used for the measurement of background activities in a sample of 9.6-kg powder. The detector system named CAGe located at the Yangyang underground laboratory was designed for measuring low levels of radioactivity from natural radioisotopes or cosmogenic nuclides such as 228 Ac, 228 Th, 226 Ra, 88 Y, and 40 K. The activities of 228 Ac and 228 Th in the powder sample were 0.88 ± 0.12 mBq/kg and 0.669 ± 0.087 mBq/kg, respectively. The activity of 226 Ra was measured to be 1.50 ± 0.23 mBq/kg. The activity of 88 Y was 0.101 ± 0.016 mBq/kg. The activity of 40 K was found as 36.0 ± 4.1 mBq/kg.