\( 4 \times \) Simplify \( 2^{-8} \div 2^{-4} \) \( 4 \times \quad A \quad \frac{1}{2^{4}} \) \( 4 \times \quad \) B \( \frac{1}{2^{32}} \) \( 4 \times \quad \) C \( 2^{2} \) \( 4 \times \quad D \quad 2^{32} \)

To simplify \( 2^{-8} \div 2^{-4} \), we can use the rule of exponents that states \( a^m \div a^n = a^{m-n} \). So, we have \( 2^{-8} \div 2^{-4} = 2^{-8 - (-4)} = 2^{-8 + 4} = 2^{-4} \). This means the expression simplifies to \( 2^{-4} \), which can be rewritten as \( \frac{1}{2^4} \). Now, multiplying by 4 gives us \( 4 \times \frac{1}{2^4} = \frac{4}{16} = \frac{1}{4} \). Hence, the answer is \( \frac{1}{2^4} \). So, the correct option is A: \( \frac{1}{2^4} \). Would you like to explore more about exponential functions and their properties? They're quite fascinating in both mathematics and science!