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To simplify the expression \( (2^{-\sqrt{3}}) \cdot 2^{-12} \) using exponent properties, you can follow these steps:
1. Use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \) to combine the exponents. In this case, we have:
\[
2^{-\sqrt{3}} \cdot 2^{-12} = 2^{-\sqrt{3} - 12}
\]
2. Therefore, the expression simplifies to:
\[
2^{-\sqrt{3} - 12}
\]
So, the equivalent expression is \( 2^{-\sqrt{3} - 12} \).