\( 4 \times \) 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 \( \quad \frac{1}{8} \) \( 4 \times \quad \) B \( \left(\frac{1}{2}\right)^{-4} \) \( 4 \times \quad \) C \( 2^{-2} \cdot 2^{-2} \) \( 4 \times \quad \) D \( 2^{2^{4}} \) \( 4 \times \quad \) E \( \frac{1}{2^{4}} \)

To find expressions equivalent to \( \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \), we note that this is the same as \( \left(\frac{1}{2}\right)^4 \), which simplifies to \( \frac{1}{2^4} = \frac{1}{16} \). The first equivalent expression is B \( \left(\frac{1}{2}\right)^{-4} \). This expression can be rewritten using the negative exponent rule, which states that \( a^{-n} = \frac{1}{a^n} \), giving us \( 2^4 = 16 \). The second equivalent expression is E \( \frac{1}{2^{4}} \). This is a direct representation of the original expression and confirms \( \frac{1}{16} \). So, the options B and E are the correct answers!