  We present a new method of studying quadruple lenses in elliptical power-law
potentials parameterized by $\psi(x,y) \propto (x^2+y^2/q^2)^{\beta/2}/\beta (0
\leq \beta < 2)$. For this potential, the moments of the four image positions
weighted by signed magnifications (magnification times parity) have very simple
properties. In particular, we find that the zeroth moment -- the sum of four
signed magnifications satisfies $\simeq 2/(2-\beta)$; the relation is exact for
$\beta=0$ (point-lens) and $\beta=1$ (isothermal potential), independent of the
axial ratio. Similar relations can be derived when a shear is present along the
major or minor axes. These relations, however, do not hold well for the
closely-related elliptical density distributions. For a singular isothermal
elliptical density distribution without shear, the sum of signed magnifications
for quadruple lenses is $\approx 2.8$, again nearly independent of the
ellipticity. For the same distribution with shear, the total signed
magnification is around 2-3 for most cases, but can be significantly different
for some combinations of the axial ratio and shear where more than four images
can appear.
