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

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To determine which expressions are equivalent to $$ \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} $$, we can simplify the original expression first.

1. **Simplifying the original expression:**
   $$
   \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \left(\frac{1}{2}\right)^4 = \frac{1^4}{2^4} = \frac{1}{16}
   $$

Now, we will evaluate each of the options to see which ones are equivalent to $$ \frac{1}{16} $$.

2. **Evaluating each option:**

- **Option A: $$ \frac{1}{8} $$**
  $$
  \frac{1}{8} \neq \frac{1}{16}
  $$

- **Option B: $$ \left(\frac{1}{2}\right)^{-4} $$**
  $$
  \left(\frac{1}{2}\right)^{-4} = 2^4 = 16 \quad \text{(not equivalent)}
  $$

- **Option C: $$ 2^{-2} \cdot 2^{2} $$**
  $$
  2^{-2} \cdot 2^{2} = 2^{-2 + 2} = 2^0 = 1 \quad \text{(not equivalent)}
  $$

- **Option D: $$ 2^{4} $$**
  $$
  2^{4} = 16 \quad \text{(not equivalent)}
  $$

- **Option E: $$ \frac{1}{2^{4}} $$**
  $$
  \frac{1}{2^{4}} = \frac{1}{16} \quad \text{(equivalent)}
  $$

3. **Conclusion:**
The expressions that are equivalent to $$ \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} $$ are:

- **E: $$ \frac{1}{2^{4}} $$**

Since we need to choose 2 options, we can see that only one option is equivalent. Therefore, the correct answer is:

- **E: $$ \frac{1}{2^{4}} $$**

None of the other options are equivalent to $$ \frac{1}{16} $$.
The expression $$ \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} $$ is equivalent to $$ \frac{1}{16} $$. Among the given options, only option E, $$ \frac{1}{2^{4}} $$, is equivalent to $$ \frac{1}{16} $$.

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

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