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