  Let $\mathbb{I}$ denote an imaginary quadratic field or the field
$\mathbb{Q}$ of rational numbers and $\mathbb{Z}_{\mathbb{I}}$ its ring of
intergers. We shall prove an explicit Baker type lower bound for
$\mathbb{Z}_{\mathbb{I}}$-linear form of the numbers \begin{equation}\label{1}
1,\ e^{\alpha_1},...,\ e^{\alpha_m},\quad m\ge 2, \end{equation} where
$\alpha_0=0$, $\alpha_1,...,\alpha_m$, are $m+1$ different numbers from the
field $\mathbb{I}$. Our work gives gives some improvements to the existing
explicit versions of of Baker's work about exponential values at rational
points. In particilar, dependences on $m$ are improved.
