2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/194247The phase-integral approximation devised by Fröman and Fröman, 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.16 pages, Revtex, to appear in Physical Review DAstrophysicsGeneral Relativity and Quantum Cosmologytext