  To elucidate the internal structure of exotic states is one of the central
purposes of hadron physics. Motivated by this, we study the electromagnetic
properties of $\bar D^{(*)}\Xi^{\prime}_c$, $\bar D^{(*)}\Lambda_c$, $\bar
D_s^{(*)}\Lambda_c$ and $\bar D_s^{(*)}\Xi_c$ pentaquarks without strange, with
strange and with double strange through QCD light-cone sum rules. We have also
evaluated electric quadrupole and magnetic octupole moments of the $\bar
D^{*}\Xi^{\prime}_c$, $\bar D^{*}\Lambda_c$, $\bar D_s^{*}\Lambda_c$ and $\bar
D_s^{*}\Xi_c$ pentaquarks. The magnetic dipole moment is the leading-order
response of a bound system to a soft external magnetic field. Thus, it ensures
a prominent platform for the examination of the internal organizations of
hadrons governed by the quark-gluon dynamics of QCD. We look forward to the
present study stimulating the interest of experimentalists in investigating the
electromagnetic properties of the hidden-charm pentaquarks.
