The problem asks to simplify the expression $12^7 \div 12^3$.

We can use the property of exponents:

$\frac{a^m}{a^n} = a^{m-n}$

So,

$12^7 \div 12^3 = 12^{7-3} = 12^4$

Thus, the simplified form is $12^4$.

The correct answer is option a. $12^4$.

Do you need any further explanation? Here are some related questions:

1. How do we simplify expressions with powers when multiplying?
2. What is the rule for dividing exponents with the same base?
3. Can we apply this rule when bases are different?
4. How do negative exponents affect simplification?
5. How do fractional exponents work in similar problems?

Tip: Always subtract exponents when dividing terms with the same base.