In addition to the explanation others have mentioned, here it is in graph form. See the where the graph of 2^x intersects the y axis (when x=0):

https://people.richland.edu/james/lecture/m116/logs/exponential.html

This also has some additional verbal explanations:

http://scienceline.ucsb.edu/getkey.php?key=2626

The simplest way I think of it is by the properties of exponentials:

2^3 / 2^2 = (2 * 2 * 2) / (2 * 2) = 2 = 2^(3-2)

Dividing two exponentials with the same base (in this case 2) is the same as that same base (2) to the power of the difference between the exponent in the numerator minus the exponent in the denominator (3 and 2 in this case).

Now lets make both exponents the same:

2^3 / 2^3 = 8/8 = 1

2^3 / 2^3 = 2^(3-3) = 2^0 = 1