The question asks which expression has a base with an exponent of 4. Let's examine the options:

1. $p + 4$: This is not an exponential expression; it involves addition.
2. $4 \cdot x \cdot y$: This is a product of numbers and variables, not an exponentiation.
3. $4^3$: This has a base of 4, but the exponent is 3, not 4.
4. $3m^4$: This has a base of $m$ with an exponent of 4.

So, the correct expression with a base and exponent of 4 is $3m^4$.

Would you like further clarification or more details? Here are 5 related questions:

1. What is an exponent?
2. How do you simplify exponential expressions?
3. How does the distributive property apply to exponents?
4. What is the difference between a base and an exponent in an expression like $2^3$?
5. How do you identify the base and exponent in a given exponential term?

Tip: When dealing with exponents, always identify the base first—it's the number or variable being raised to a power.