We define a sample of 62 galaxies in the Chandra Deep Field-North whose Spitzer IRAC SEDs exhibit the characteristic power-law emission expected of luminous AGN. We study the multiwavelength properties of this sample, and compare the AGN selected in this way to those selected via other Spitzer color-color criteria. Only 55% of the power-law galaxies are detected in the X-ray catalog at exposures of >0.5 Ms, although a search for faint emission results in the detection of 85% of the power-law galaxies at the > 2.5 sigma detection level. Most of the remaining galaxies are likely to host AGN that are heavily obscured in the X-ray. Because the power-law selection requires the AGN to be energetically dominant in the near- and mid-infrared, the power-law galaxies comprise a significant fraction of the Spitzer-detected AGN population at high luminosities and redshifts. The high 24 micron detection fraction also points to a luminous population. The power-law galaxies comprise a subset of color-selected AGN candidates. A comparison with various mid-infrared color selection criteria demonstrates that while the color-selected samples contain a larger fraction of the X-ray luminous AGN, there is evidence that these selection techniques also suffer from a higher degree of contamination by star-forming galaxies in the deepest exposures. Considering only those power-law galaxies detected in the X-ray catalog, we derive an obscured fraction of 68% (2:1). Including all of the power-law galaxies suggests an obscured fraction of < 81% (4:1).