One interpretation for a power of natural numbers, such as , is that it is counting a certain collection of functions: in this case, the number of functions from a six-element set to a ten-element set. (One way to think about it is that
is the number of six-digit combinations from 000000 to 999999, and each combination corresponds to a function from
to
: the first digit is the image of
, the second digit is the image of
, etc.)
In general, the number is the number of functions from an
-element set to a
-element set. This is somewhat analogous to standard interpretations of other arithmetical operations: