To solve the expression [tex]\(\left(8^{2 / 3}\right)^{1 / 2}\)[/tex], we'll break it down step-by-step:
1. Calculate the inner exponent:
[tex]\[
8^{2 / 3}
\][/tex]
2. Simplify the base exponentiation:
Recall that [tex]\(8\)[/tex] can be written as [tex]\(2^3\)[/tex]. So we have:
[tex]\[
8^{2 / 3} = (2^3)^{2 / 3}
\][/tex]
3. Use the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
Applying this property, we get:
[tex]\[
(2^3)^{2 / 3} = 2^{3 \cdot (2 / 3)} = 2^2 = 4
\][/tex]
4. Now take the outer exponentiation:
[tex]\[
(4)^{1 / 2}
\][/tex]
5. Simplify the outer exponent:
[tex]\[
4^{1 / 2} = \sqrt{4} = 2
\][/tex]
Thus, the value of the expression [tex]\(\left(8^{2 / 3}\right)^{1 / 2}\)[/tex] is [tex]\(2\)[/tex].
Therefore, the correct answer is:
C. 2
