  We consider a class of 5-D brane-world solutions with a power-law warp factor
$a(y)\propto y^{q}$, and bulk dilaton with profile $\phi \propto \ln y$, where
$y$ is the proper distance in the extra dimension. This class includes the
Heterotic M-theory brane-world of Refs. \cite{ovrut,ekpy} and the
Randall-Sundrum (RS) model as a limiting case. In general, there are two moduli
fields $y_{\pm}$, corresponding to the "positions" of two branes (which live at
the fixed points of an orbifold compactification). Classically, the moduli are
massless, due to a scaling symmetry of the action. However, in the absence of
supersymmetry, they develop an effective potential at one loop. Local terms
proportional to $K_\pm^4$, where $K_\pm=q/y_\pm$ is the local curvature scale
at the location of the corresponding brane, are needed in order to remove the
divergences in the effective potential. Such terms break the scaling symmetry
and hence they may act as stabilizers for the moduli. When the branes are very
close to each other, the effective potential induced by massless bulk fields
behaves like $V\sim d^{-4}$, where $d$ is the separation between branes. When
the branes are widely separated, the potentials for each one of the moduli
generically develop a "Coleman-Weinberg"-type behaviour of the form
$a^4(y_\pm)K_\pm^4 \ln(K_\pm/\mu_\pm)$, where $\mu_\pm$ are renormalization
scales. In the RS case, the bulk geometry is $AdS$ and $K_\pm$ are equal to a
constant, independent of the position of the branes, so these terms do not
contribute to the mass of the moduli. However, for generic warp factor, they
provide a simple stabilization mechanism. For $q\gtrsim 10$, the observed
hierarchy can be naturally generated by this potential, giving the lightest
modulus a mass of order $m_- \lesssim TeV$.
