There has been growing interest in the possibility of testing more precisely the assumption of statistical isotropy of primordial density perturbations. If it is to be tested with galaxy surveys at distance scales < or = 10 Mpc, then nonlinear evolution of anisotropic power must be understood. To this end, we calculate the angular dependence of the power spectrum to third order in perturbation theory for a primordial power spectrum with a quadrupole dependence on the wave vector direction. Our results suggest that primordial power anisotropies will be suppressed by < or = 7% in the quasilinear regime. We also show that the skewness in the statistically anisotropic theory differs by no more than 1% from that in the isotropic theory.
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