  We construct the Drinfeld twists (or factorizing $F$-matrices) of the
supersymmetric model associated with quantum superalgebra $U_q(gl(m|n))$, and
obtain the completely symmetric representations of the creation operators of
the model in the $F$-basis provided by the $F$-matrix. As an application of our
general results, we present the explicit expressions of the Bethe vectors in
the $F$-basis for the $U_q(gl(2|1))$-model (the quantum t-J model).
