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We perform a systematic study of the electromagnetic properties of exotic states to shed light on their nature, which is still controversial and not fully understood. The magnetic dipole and higher multipole moments of a hadronic state are as fundamental a dynamical quantity as its mass, and they contain valuable information about the deep structure underlying it. In the present work, we have explored the magnetic dipole and higher multipole moments of the hidden-charm pentaquarks with quantum number J P = 3 / 2 − using the QCD light-cone sum rule method and different interpolating currents. The obtained results show that different interpolating currents employed to probe pentaquarks with the same quark content produce varying results for their magnetic dipole and higher multipole moments at all. This can be interpreted to mean that there is more than one hidden-charm pentaquark with identical quark content but with different magnetic dipole and higher multipole moments. The nature, internal structure, and quark-gluon configurations of these states can be better understood by studying their electromagnetic properties. [ABSTRACT FROM AUTHOR]