= Solution
For $h\nu\ll k_BT$, expand the exponential in the <thermal free-free emissivity>:
$$
e^{-h\nu/(k_BT)}=1-\frac{h\nu}{k_BT}+O\!\left(\frac{h^2\nu^2}{k_B^2T^2}\right).
$$
The <energy> emitted per unit <frequency> is therefore approximately flat, with the weak <Gaunt factor> dependence superposed. At these low <photon> <energies>, most of the thermal <electrons> can participate in emission; there is no exponentially small population threshold.
For $h\nu>k_BT$, the spectrum turns down approximately as $e^{-h\nu/(k_BT)}$, apart from the <Gaunt factor>. <Conservation of energy> requires an emitting <electron> to supply at least $h\nu$. The high-<energy> tail of its <Maxwell-Boltzmann distribution> is exponentially rare, which produces this cutoff.
“Flat” refers to $j_\nu$, an <energy> spectrum per unit <frequency>. The emitted <photon> number spectrum instead contains $1/(h\nu)$, while <energy> per logarithmic <frequency> interval is $\nu j_\nu$. At sufficiently low <frequency> the <plasma> can also become <optically thick> to <free-free absorption>; the given optically thin emissivity is then not the escaping spectrum.
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