  We study in detail the power spectra of scalar and tensor perturbations
generated during inflation in loop quantum cosmology (LQC). After clarifying in
a novel quantitative way how inverse-volume corrections arise in inhomogeneous
settings, we show that they can generate large running spectral indices, which
generally lead to an enhancement of power at large scales. We provide explicit
formulae for the scalar/tensor power spectra under the slow-roll approximation,
by taking into account corrections of order higher than the runnings. Via a
standard analysis, we place observational bounds on the inverse-volume quantum
correction \delta ~ a^{- \sigma} (\sigma >0, $a$ is the scale factor) and the
slow-roll parameter \epsilon_V for power-law potentials as well as exponential
potentials by using the data of WMAP 7yr combined with other observations. We
derive the constraints on \delta for two pivot wavenumbers k_0 for several
values of \delta. The quadratic potential can be compatible with the data even
in the presence of the LQC corrections, but the quartic potential is in tension
with observations. We also find that the upper bounds on \delta (k_0) for given
\sigma and k_0 are insensitive to the choice of the inflaton potentials.
