We present low-temperature measurements of the ballistic transport in high-quality quantum wires. As the Fermi energy is varied, the conductance of these wires exhibits quantized plateaus at values lower than integer multiples of 2e(2)/h. We observe Luttinger liquid power laws in the temperature dependence of the plateau conductances as well as in the non-linear current-voltage characteristics. From these power laws we extract the Luttinger liquid scaling exponent alpha(N) as a function of the Fermi energy and the number of occupied subbands. (C) 2000 Elsevier Science B.V. All lights reserved.