Question

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

(1 point)
Responses

2–√
square root of 2

212
2 raised to the 1 half power

22
2 squared

2

Answer 1

To simplify the expression \((2^{-\sqrt{}})^3 \cdot 2^{-12}\), we can use the properties of exponents.

1. Start by applying the exponent to \(2^{-\sqrt{}}:\)
\[
(2^{-\sqrt{}})^3 = 2^{-3\sqrt{}}
\]

2. Now, multiply this by \(2^{-12}: \)
\[
2^{-3\sqrt{}} \cdot 2^{-12} = 2^{-3\sqrt{} - 12}
\]

Since the options given are not numeric and are referred to in a different way, let's analyze the options with respect to our result to see if any match the simplified form.

Given the four options:
1. \(2^{-\sqrt{}} = \sqrt{2}\)
2. \(2^{1/2}\)
3. \(2^{2}\)
4. \(2\)

Since all options deal with \(2^x\) format, we can evaluate the quantities by just looking for equality among the obstrusive powers or typical $(-n)$ associated with square roots or integers.

If we need further simplifications or direct identification, it's needed to either derive more or convert terms while recognizing property utilizations in exponents.

However, my general simplification yields:

\[
-3\sqrt{} - 12
\]

None of the given options directly, but \(2^{-12}\) stays prominent here unless evaluated or altogether established against existing square values. Therefore, specifically in focusing direct actions might it originally represent equivalently \(2^{-12}\) when simplified.

In summation, simply re-evaluating over beforehand selections or bases of 2 can reveal direct ratios or applies to common ground numbers to correlate correctly to solid numbers, but yielding outright value into all expressions at base may also yield factorization just needing link against values or inversions specified.

Considering that, there currently isn't an immediate pair equivalent focusing to simplify terms back against pure integers specified.