Problem #PRU-100365

Problem

You have 26 constants, labeled $A$ through $Z$. Let $A$ equal 1. The other constants have values equal to the letter’s position in the alphabet, raised to the power of the previous constant. That means that $B$ (the second letter) = $2^A=2^1=2$, $C=3^B=3^2=9$, and so on. Find the exact numerical value for this expression: $$(X-A)(X-B)(X-C)\dots (X-Y)(X-Z).$$