To solve $4^3 \cdot 4^2$, we can apply the rule of exponents that states when multiplying two powers with the same base, we add the exponents. So,

$4^3 \cdot 4^2 = 4^{3+2} = 4^5$

Now, calculating $4^5$:

$4^5 = 1024$

Therefore, the answer is:

$4^3 \cdot 4^2 = 1024$

Would you like further details or have any questions?

Here are some related questions:

1. How would this change if we had $4^3 \cdot 4^4$?
2. What is the rule for dividing powers with the same base?
3. How do we handle powers with different bases, like $3^2 \cdot 4^3$?
4. What if we had a negative base, such as $(-4)^3 \cdot (-4)^2$?
5. How can we express $4^5$ as a product of primes?

Tip: When multiplying powers with the same base, remember to add the exponents for a quick calculation.