You can use numpy.power.outer:
>>> K=9
>>> numpy.power.outer(numpy.array([1, 4, 5]), numpy.arange(1, K+1)).T
array([[ 1, 4, 5],
[ 1, 16, 25],
[ 1, 64, 125],
[ 1, 256, 625],
[ 1, 1024, 3125],
[ 1, 4096, 15625],
[ 1, 16384, 78125],
[ 1, 65536, 390625],
[ 1, 262144, 1953125]])