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To simplify the expression \( (2^{-\sqrt{}})^3 \cdot 2^{-12} \) using exponent properties, we can follow these steps:
1. **Apply the exponent to the first term:**
\[
(2^{-\sqrt{}})^3 = 2^{-3\sqrt{}}
\]
2. **Now our expression looks like this:**
\[
2^{-3\sqrt{}} \cdot 2^{-12}
\]
3. **Use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \):**
\[
2^{-3\sqrt{}} \cdot 2^{-12} = 2^{-3\sqrt{} - 12}
\]
Thus, the expression \( (2^{-\sqrt{}})^3 \cdot 2^{-12} \) simplifies to:
\[
2^{-3\sqrt{} - 12}
\]
This is the final equivalent expression. If you have specific response options to compare, you can now evaluate them against \( 2^{-3\sqrt{} - 12} \).