I'm trying to create a floating point output raster with Raster Calculator in ArcMap 10.2.2. If I enter the equation: 0.99^[inputRaster], I get an integer raster as the output and all cells equal zero. The inputRaster has values from -900 to 33,000.

Thank you for your help!

'^' means Boolean XOr in Map Algebra notation (see here for more), which is giving you the correct output - all zeroes because both 0.99 and your raster are 'True'. To raise something to an exponent, you want 0.99 ** "inputRaster"