  The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used
for computing cosmological perturbations in the power-law inflationary model.
The phase-integral formulas for the scalar and tensor power spectra are
explicitly obtained up to ninth-order of the phase-integral approximation. We
show that, the phase-integral approximation exactly reproduces the shape of the
power spectra for scalar and tensor perturbations as well as the spectral
indices. We compare the accuracy of the phase-integral approximation with the
results for the power spectrum obtained with the slow-roll and uniform
approximation methods.
