Using a sample of 1.06 times 10^8 psi^{prime} decays collected by the BESIII detector, chi_{c0} and chi_{c2} decays into pi^0pi^0 and etaeta are studied. The branching fraction results are Br(chi_{c0}topi^0pi^0)=(3.23pm 0.03pm0.23 pm 0.14)times 10^{-3}, Br(chi_{c2}topi^0pi^0)=(8.8pm 0.2pm 0.6pm0.4)times 10^{-4}, Br(chi_{c0}toetaeta)=(3.44pm 0.10pm0.24 pm0.2)times 10^{-3}, and Br(chi_{c2}toetaeta)=(6.5pm 0.4pm 0.5pm 0.3)times 10^{-4}, where the uncertainties are statistical, systematic due to this measurement, and systematic due to the branching fractions of psi^{prime}togammachi_{cJ}, respectively. The results provide information on the decay mechanism of chi_c states into pseudoscalars.
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