Let's go through each of the expressions and solve them step by step using the division rule for scientific notation:

$\frac{A \times 10^m}{B \times 10^n} = \frac{A}{B} \times 10^{m-n}$

Solutions:

1. $8 \times 10^8 \div 2 \times 10^4$
   $\frac{8}{2} \times 10^{8-4} = 4 \times 10^4$

2. $8 \times 10^{12} \div 8 \times 10^9$
   $\frac{8}{8} \times 10^{12-9} = 1 \times 10^3$

3. $9 \times 10^6 \div 3 \times 10^3$
   $\frac{9}{3} \times 10^{6-3} = 3 \times 10^3$

4. $5 \times 10^{-8} \div 1 \times 10^{-4}$
   $\frac{5}{1} \times 10^{-8 - (-4)} = 5 \times 10^{-4}$

5. $6 \times 10^{-7} \div 2 \times 10^{-2}$
   $\frac{6}{2} \times 10^{-7 - (-2)} = 3 \times 10^{-5}$

6. $1 \times 10^6 \div 2 \times 10^3$
   $\frac{1}{2} \times 10^{6-3} = 0.5 \times 10^3$ Alternatively, writing in proper scientific notation:
   $5 \times 10^2$

Would you like a detailed explanation for any of the steps?

Here are 5 related questions to expand your understanding:

1. How do you convert a number into scientific notation?
2. What is the difference between multiplying and dividing numbers in scientific notation?
3. Why do we subtract exponents when dividing powers of ten?
4. How would you handle division if the coefficients (A and B) resulted in a decimal?
5. Can you rewrite $0.5 \times 10^3$ in standard form?

Tip: When dealing with negative exponents, remember that $10^{-n}$ means "1 divided by $10^n$."