How do you make 29 using 1 2 3 4 only once?

Not possible !... Since 29 is a Prime number - you'd need to make either 28 or 30 with the remaining three numbers in order to add or subtract 1.

The above is not true, there are 2 ways to do this.

a) 4-1 =3; 3 to the power of (the other) 3 is 27 and then add 2 = 29.

b) 4+1=5; 2 to the power of the 5 is 32, then take off 3 = 29