Motivated by the recent experiment by Grayson et.al., we investigate a non-ohmic current-voltage characteristics for the tunneling into fractional quantum Hall liquids. We give a possible explanation for the experiment in terms of the chiral Tomonaga-Luttinger liquid theory. We study the interaction between the charge and neutral modes, and found that the leading order correction to the exponent $alpha$ $(Isim V^alpha)$ is of the order of $sqrt{epsilon}$ $(epsilon=v_n/v_c)$, which reduces the exponent $alpha$. We suggest that it could explain the systematic discrepancy between the observed exponents and the exact $alpha =1/ u$ dependence.
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