To solve the equation $10^3 \cdot 10^4$, we need to apply the rule for multiplying powers with the same base. The rule states that:

$a^m \cdot a^n = a^{m+n}$

In this case, the base is 10, and the exponents are 3 and 4. We add the exponents together:

$10^3 \cdot 10^4 = 10^{3+4} = 10^7$

Therefore, the answer is:

$10^3 \cdot 10^4 = 10^7$

Would you like further details on this topic or have any questions?

Here are some related questions you might find helpful:

1. What is the rule for dividing powers with the same base?
2. How do you handle exponents when raising a power to another power?
3. What happens when you multiply numbers with different bases but the same exponent?
4. Can you explain the zero exponent rule?
5. What is the negative exponent rule?

Tip: When multiplying powers with the same base, always add the exponents.