The problem asks which value is equivalent to $2^3 \cdot 2^2$.

Let's solve this step by step:

1. Calculate each power of 2: $2^3 = 2 \times 2 \times 2 = 8$ $2^2 = 2 \times 2 = 4$

2. Multiply the results: $8 \times 4 = 32$

So, the value equivalent to $2^3 \cdot 2^2$ is 32.

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the rule for multiplying powers with the same base?
2. How would the solution change if the base were 3 instead of 2?
3. How do you simplify $2^5$ directly without splitting it into smaller parts?
4. What is the product of $2^4 \cdot 2^3$?
5. How does exponentiation behave with negative exponents?

Tip: When multiplying exponents with the same base, add the exponents (e.g., $a^m \cdot a^n = a^{m+n}$).