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We present dust continuum observations of the protoplanetary disk surrounding the pre-main-sequence star AS 209, spanning more than an order of magnitude in wavelength from 0.88 to 9.8 mm. The disk was observed with subarcsecond angular resolution (0".2-0".5) to investigate radial variations in its dust properties. At longer wavelengths, the disk emission structure is notably more compact, providing model-independent evidence for changes in the grain properties across the disk. We find that physical models which reproduce the disk emission require a radial dependence of the dust opacity Kappa sub([nu]). Assuming that the observed wavelength-dependent structure can be attributed to radial variations in the dust opacity spectral index ( beta ), we find that beta (R) increases from beta < 0.5 at ~20 AU to beta > 1.5 for R [> ~] 80 AU, inconsistent with a constant value of beta across the disk (at the 10[sigma] level). Furthermore, if radial variations of Kappa sub([nu]) are caused by particle growth, we find that the maximum size of the particle-size distribution (a sub(max)) increases from submillimeter-sized grains in the outer disk (R [> ~]> 70 AU) to millimeter- and centimeter-sized grains in the inner disk regions (R [<, ~] 70 AU). We compare our observational constraint on a sub(max)(R) with predictions from physical models of dust evolution in protoplanetary disks. For the dust composition and particle-size distribution investigated here, our observational constraints on a sub(max)(R) are consistent with models where the maximum grain size is limited by radial drift.