Let's simplify the expression $2^{-8} \div 2^{-4}$:

Using the law of exponents, which states:

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

We can rewrite the division as:

$2^{-8} \div 2^{-4} = 2^{-8 - (-4)} = 2^{-8 + 4} = 2^{-4}$

Thus, the simplified expression is:

$2^{-4} = \frac{1}{2^4} = \frac{1}{16}$

Now, looking at the answer choices:

• Option A: $\frac{1}{2^4}$ is the correct answer.

Would you like any further clarification on this problem or more details?

Here are 5 related questions you might find useful:

1. How do you simplify expressions involving negative exponents?
2. What are some real-life applications of exponent rules?
3. How would the problem change if the bases were different but still powers of 2?
4. Can you explain other exponent laws, like the power of a power rule?
5. What happens if we multiply terms with exponents instead of dividing?

Tip: Always remember that negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent.