FOM: Hint

[Fred Johnson]

Bell and Machover (A Course in Mathematical Logic) use the
following sentence to illustrate the differences between 
the Platonist (sentences-are-about-structures) and the 
constructivist (sentences-are-about-activities) views of 
mathematical sentences:
   There are irrational real numbers a and b such that 
   a with exponent b is rational.  (p. 402)
They give a simple Platonist proof that shows that it (taken 
Platonically) is true.  Is there a constructivist proof
that shows that it (taken constructively) is true?
If so, please give me a hint.
Thanks, Fred Johnson