There are many expressions that have a base with an exponent of 4, but some examples include:
1. x^4
2. (2y)^4
3. (3z - 1)^4
4. (a + b)^4
5. 16t^4
In each of these expressions, the base (x, 2y, 3z - 1, a + b, and 16t) is raised to the fourth power (exponent of 4).