We present new spatially resolved observations of the dust thermal emission at 7 mm from the Fomalhaut debris disk obtained with the Australia Telescope Compact Array .
These observations provide the longest wavelength detection of the Fomalhaut debris disk to date .
We combined the new data to literature sub-mm data to investigate the spectral index of the dust thermal emission in the sub-millimeter and constrained the q -slope of the power-law grain size distribution .
We derived a value for q = 3.48 \pm 0.14 for grains with sizes around 1 mm .
This is consistent with the classical prediction for a collisional cascade at the steady-state .
The same value can not be explained by more recent collisional models of planetesimals in which either the velocity distribution of the large bodies or their tensile strength is a strong function of the body size .