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

Let's break it down in a fun way! When you divide powers of the same base, you subtract the exponents. So, \( 2^{-8} \div 2^{-4} \) becomes \( 2^{-8 - (-4)} \), which simplifies to \( 2^{-4} \). Now, multiplying \( 4 \) (which is \( 2^2 \)) by \( 2^{-4} \) gives you \( 4 \times 2^{-4} = 2^2 \times 2^{-4} = 2^{2 - 4} = 2^{-2} \). That's equal to \( \frac{1}{2^2} \) or \( \frac{1}{4} \). Here’s a nifty little tip: Always remember that when you multiply or divide terms with the same base, just deal with the exponents! It's like a power dance - just keep it smooth and subtract or add as needed! And for convenience's sake, if you come across terms that confuse you with negative exponents, think of them as "the reciprocal" of the positive exponent. It's a little mind trick to keep your calculations feeling light and breezy!