  Approximate scaling laws with respect to the nuclear charge are introduced
for the time-dependent Dirac equation describing hydrogen-like ions subject to
laser fields within the dipole approximation. In particular, scaling relations
with respect to the laser wavelengths and peak intensities are discussed. The
validity of the scaling relations is investigated for two-, three-, four-, and
five-photon ionization of hydrogen-like ions with the nuclear charges ranging
from $Z=1$ to $92$ by solving the corresponding time-dependent Dirac equations
adopting the properly scaled laser parameters. Good agreement is found and thus
the approximate scaling relations are shown to capture the dominant effect of
the response of highly-charged ions to intense laser fields compared to the one
of atomic hydrogen. On the other hand, the remaining differences are shown to
allow for the identification and quantification of additional, purely
relativistic effects in light-matter interaction.
