  Relativistic heavy ion collisions provide a unique opportunity to study the
shape of colliding nuclei, even up to higher-order multiple deformations. In
this work, several observables that are sensitive to quadrupole and
hexadecapole deformations of Uranium-238 in relativistic U+U collisions have
been systematically investigated with A Multi-Phase Transport model. We find
that the flow harmonic $v_{2}$, the $v_{2}$ and mean transverse momentum
correlation, and the three-particle asymmetry cumulant ${\rm ac}_{2}\{3\}$ are
sensitive to nuclear quadrupole deformation, while ${\rm ac}_{2}\{3\}$ and
nonlinear response coefficient $\chi_{4,22}$ are sensitive to nuclear
hexadecapole deformation. Our results from transport model studies are in
qualitative agreement with previous hydrodynamic studies. The results indicate
that the uncertainties of the hexadecapole deformation of Uranium on the
quadrupole deformation determination can be reduced by the abundance of
correlation observables provided by the relativistic heavy ion collisions.
