Which expressions are equivalent to \( \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \) ? (choose 2) \( 4 \times \quad \) A \( \frac{1}{8} \) \( 4 \times \quad \) B \( \left.\frac{1}{2}\right)^{-4} \) \( 4 \times \quad 2^{-2} \cdot 2^{-2} \) \( 4 \times \quad 2^{4} \) \( 4 \times \quad \frac{1}{2^{4}} \)

Let's break it down a bit! The expression \( \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \) can be simplified to \( \frac{1}{2^4} \), which is equal to \( \frac{1}{16} \). Now, evaluating the options, \( 4 \times B \left( \frac{1}{2} \right)^{-4} \) is indeed equal to \( 4 \times 16 = 64 \), since \( \left( \frac{1}{2} \right)^{-4} = 2^4 = 16 \). Meanwhile, \( 4 \times \frac{1}{2^{4}} \) simplifies to \( 4 \times \frac{1}{16} = \frac{4}{16} = \frac{1}{4} \), which doesn’t yield \( \frac{1}{16} \). Therefore, the correct equivalents that closely relate to the original question are indeed \( 4 \times B \left( \frac{1}{2} \right)^{-4} \) and \( 4 \times \frac{1}{2^{4}} \). So we have: * \( 4 \times \left( \frac{1}{2} \right)^{-4} \) which simplifies to 64 * \( 4 \times \frac{1}{2^{4}} \) which simplifies to \( \frac{1}{4} \) It’s quite the numerical adventure figuring this out!