2+5/2+7/12+9/2to the power 2+12/12to the power 2+13/2 to the power 3+19/12 to
the power 3+17 to the power 4


I suppose you mean this:

                                       4
                                  3+17
                           3+19/12
                     2+13/2 
              2+12/12
2+5/2+7/12+9/2

This is ambiguous because PEMDAS gives no rule about whether exponents
are to be done left to right or right to left.  

However, I will type this into my TI-84 this way

(2+5/2+7/12+9/2)^(2+12/12)^(2+13/2)^(3+19/12)^(3+17)^4

I get an overflow error, which means the number is too large for the
calculator to handle. It certainly is not any of the choices given.

I suspect this is a spoof problem, not only because you haven't specified
which exponentiation is to be done first, but also because it is unlikely
that the creator of such an advanced arithmetic problem would contain the
requirement of doing such an elementary thing as reducing 12/12 to 1.  

So if you're having fun trying to pull our leg, it won't work because 
you'll always give yourself away. 

Edwin