text: Powers of a number with absolute value less than one tend to zero:
  as  when
  Any power of one is always one:
  for all  if
  Powers of  alternate between  and  as  alternates between even and odd, and thus do not tend to any limit as  grows.
  If ,  alternates between larger and larger positive and negative numbers as  alternates between even and odd, and thus does not tend to any limit as  grows.
  If the exponentiated number varies while tending to  as the exponent tends to infinity, then the limit is not necessarily one of those above. A particularly important case is
  as
  See  below.
  Other limits, in particular those of expressions that take on an indeterminate form, are described in  below.
  Power functions
  Real functions of the form , where , are sometimes called power functions. When  is an integer and , two primary families exist: for  even, and for  odd. In general for , when  is even  will tend towards positive infinity with increasing , and also towards positive infinity with decreasing . All graphs from the family of even power functions have the general shape of , flattening more in the middle as  increases. Functions with this kind of symmetry  are called even functions.