How do you identify the base and exponent in the expression two to third power?

The base is the large number, and is the number being multiplied; the exponent is the smaller number on the upper right, which says how many times the base is multiplied. 23 says that 2 is multiplied 3 times, so: 2 X 2 X 2.

In this case, the base is 2, and the exponent is 3.