Using the exponent properties, which of the following expressions is equivalent to (2–√)3×2−12

Let's solve both questions one at a time using exponent properties.

### Question 1:
You need to simplify the expression \((2^{-\sqrt{}})^{3} \times 2^{-12}\).

1. Apply the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\). Thus,
\[
(2^{-\sqrt{}})^{3} = 2^{-3\sqrt{}}
\]
2. Now, combine it with the other term:
\[
2^{-3\sqrt{}} \times 2^{-12} = 2^{-3\sqrt{} - 12}
\]
3. Unfortunately, without knowing the actual value of \(-\sqrt{}\), we cannot simplify this expression further explicitly. However, we can imply it takes a form depending on \(-3\sqrt{} - 12\).

Now, if you interpret \(-\sqrt{}\) as \( -1\), calculating it would yield different results. However, based on the provided responses, which consist of numerical powers of 2, we evaluate the closest option that aligns with the simplification or value \(2^{-k}\) would render invariant under specific conditions.

### Question 2:
You need to simplify the expression \(2^{16} \sqrt[3]{2^{7}}^{13}\).

1. Rewrite the term \(\sqrt[3]{2^{7}}^{13}\) using the power of a power property:
\[
\sqrt[3]{2^{7}}^{13} = (2^{7})^{13/3} = 2^{7 \cdot (13/3)} = 2^{\frac{91}{3}}
\]
2. Combine with \(2^{16}\):
\[
2^{16} \times 2^{\frac{91}{3}} = 2^{16 + \frac{91}{3}}
\]
3. To add these exponents:
Convert 16 to a fraction with a common denominator of 3:
\[
16 = \frac{48}{3}
\]
Now add:
\[
\frac{48}{3} + \frac{91}{3} = \frac{139}{3}
\]
4. Thus, the expression simplifies to:
\[
2^{\frac{139}{3}}
\]

Based on the responses you provided, unless you have an arithmetic consideration directly to pick as a standard multiple of available options, the expression \(2^{\frac{139}{3}}\) ultimately returns as a systematic answer, but may not precisely render direct responses if not within \(2^k\) range.

If you need further refinement or comparison per provided results fulfilling requests, they’ll rely on the contextual base of exponent nature derived and interpreted finite range present within original variables.

In conclusion, the answers related to each question seem to elude exacting direct matches considering provided responses unless squared or value indices are highly evaluated which when matched against algebraic derivations circumnavigated within dimensional exponents.