  Using the Fronsdal-Galindo formula for the exponential mapping from the
quantum algebra $U_{p,q}(gl(2))$ to the quantum group $GL_{p,q}(2)$, we show
how the $(2j+1)$-dimensional representations of $GL_{p,q}(2)$ can be obtained
by `exponentiating' the well-known $(2j+1)$-dimensional representations of
$U_{p,q}(gl(2))$ for $j$ $=$ $1,{3/2},... $; $j$ $=$ 1/2 corresponds to the
defining 2-dimensional $T$-matrix. The earlier results on the
finite-dimensional representations of $GL_q(2)$ and $SL_q(2)$ (or $SU_q(2)$)
are obtained when $p$ $=$ $q$. Representations of $U_{\bar{q},q}(2)$ $(q$ $\in$
$\C \backslash \R$ and $U_q(2)$ $(q$ $\in$ $\R \backslash \{0\})$ are also
considered. The structure of the Clebsch-Gordan matrix for $U_{p,q}(gl(2))$ is
studied. The same Clebsch-Gordan coefficients are applicable in the reduction
of the direct product representations of the quantum group $GL_{p,q}(2)$.
