(A,B,C) is a 'pandigital' set of positive integers where the concatenated A|B|C is comprised of all, and only, the ten decimal digits (0 to 9) with no repeated digits. (In the following, except where the base number has a radix, all integers are in base 10.)
How many of these 'pandigital' sets exist for

- A
_{B} = C [*A in base B equals C*]
- A
^{B} = C [*A to the power of B equals C*]

Provide a separate value for each specification.