Using the exponent properties, which of the following expressions is equivalent to (√2)^3 * 2−^1/2

Let's simplify the expression \((\sqrt{2})^3 \cdot 2^{-1/2}\) using properties of exponents.

1. First, rewrite \(\sqrt{2}\) as \(2^{1/2}\):
\[
(\sqrt{2})^3 = (2^{1/2})^3
\]
Using the property of exponents \((a^m)^n = a^{mn}\), we get:
\[
(2^{1/2})^3 = 2^{(1/2) \cdot 3} = 2^{3/2}
\]

2. Next, we include the second part of the expression:
\[
2^{3/2} \cdot 2^{-1/2}
\]
Using the property \(a^m \cdot a^n = a^{m+n}\), we combine the exponents:
\[
2^{3/2 - 1/2} = 2^{(3/2) - (1/2)} = 2^{(3/2 - 1/2)} = 2^{2/2} = 2^1
\]
Therefore, we have:
\[
2^1 = 2
\]

Thus, the equivalent expression to \((\sqrt{2})^3 \cdot 2^{-1/2}\) is \(2\).

The correct answer is:
\[
\boxed{2}
\]