Question

Using the exponent properties, which of the following expressions is equivalent to (2–√)3⋅2−12 ?(1 point) Responses

Answer 1

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 \( 2^{-3\sqrt{} - 12} \).