High-pressure single-crystal/powder synchrotron X-ray diffraction was carried out on a hydrous pure magnesium pyrope (Mg3Al2Si3O2) containing 900 ppmw H2O, synthesized at 4.0 GPa and 1300 K. The pressure-volume (P-V) single-crystal data from room pressure to 9.81 GPa at ambient temperature were fitted by a third-order Birch-Murnaghan equation of state (BM-EoS) yielding a unit-cell volume of V-0 = 1505.14 +/- 0.38 angstrom(3), an isothermal bulk modulus of K-0 = 160 +/- 3 GPa and its pressure derivative K'(0) = 5.2 +/- 0.4. When fixing K'(0) = 4.0, the data yielded V-0 = 1504.58 +/- 0.32 angstrom 3 and K-0 =166 +/- 2 GPa. The pressure-volume-temperature (P-V-7) EoS of the synthetic hydrous pyrope was also measured at temperatures up to 900 K and pressures up to 16.75 GPa, using a diamond anvil cell in conjunction with in situ synchrotron angle-dispersive powder X-ray diffraction. The P-V data at room temperature and in a pressure range of 0.0001-14.81 GPa were then analyzed by a third-order BM-EoS and yielded V-0 = 1505.35 +/- 0.25 angstrom(3), K-0 = 161 +/- 2 GPa, K'(0) = 5.0 +/- 0.3. With K'(0) fixed to 4.0, we also obtained V-0 = 1505.04 +/- 0.29 angstrom(3) and K-0 =167 +/- 1 GPa. Consequently, we fitted the P-V-T data with the high temperature third -order BM-EoS approach and obtained the thermoelastic parameters of single-crystal/powder V-0 = 1505.4 +/- 0.3 angstrom(3), K-0 = 162 +/- 1GPa, K-0 = 4.9 +/- 0.2, the temperature derivative of the bulk modulus (partial derivative K-0/partial derivative T)(p)= -0.018 +/- 0.004 GPa K-1, and the thermal expansion coefficient at ambient conditions alpha(0)= (3.2 +/- 0.1) x 10(-5) K-1. These properties were consistent with the thermal pressure EoS analysis. These new results on hydrous pyrope were also compared with previous studies of anhydrous pyrope. The main effect of hydration on pyrope is to decrease Ko and increase K'(0) by increasing the vacancies or unoccupied volume in the structure. The entire dataset enabled us to examine the thermoelastic properties of important mantle garnets and this data has further applications for modeling the P-T conditions in the upper mantle of the Earth's interior using deep mineral assemblages. (C) 2017 Published by Elsevier B.V.