Problem #PRU-100365

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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: \[(X-A)(X-B)(X-C)\dots (X-Y)(X-Z).\]