zoom is not magnification. zoom is actually a somewhat meaningless number that is the result of dividing the longest focal length that the lens can reach by the shortest focal length that the lens can reach. as about 43 mm is normal for a 35 mm camera, any lens that starts wider than 43 (and all of the fixed lens cameras do), will not magnify by the zoom number.
43 normal
86 twice as close (half the distance)
172 (1/4 the distance)
336 (1/8 the distance)
etc.
additionally, because some cameras start wider than others (28 mm wide vs 35 mm wide), a camera that starts wide could have a larger zoom number but still have the same length at the long end, or a camera could have the same zoom number and come up shorter on the long end.
anyway, the rule of thumb is that 1/focal length is the fastest reliable hand held shutter speed. so at the 504 mm focal length of the olympus SP-550UZ 1/500th is the standard shutter speed. the sensor shift image stabilization should allow another two stops (1/500 --> 1/250 ---> 1/125) for reliable handholding. which is good enough for ISO 100 sensitivity in bright daylight.