To find the value of the expression [tex]\(\left\{64^3\right\}^{1 / 6}\)[/tex], we can simplify it step by step using properties of exponents.
First, let's rewrite the given expression:
[tex]\[
\left(64^3\right)^{1/6}
\][/tex]
Using the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex], we can combine the exponents:
[tex]\[
(64^3)^{1/6} = 64^{3 \cdot \frac{1}{6}}
\][/tex]
Now, multiply the exponents:
[tex]\[
64^{3 \cdot \frac{1}{6}} = 64^{1/2}
\][/tex]
The expression [tex]\(64^{1/2}\)[/tex] represents the square root of 64:
[tex]\[
64^{1/2} = \sqrt{64}
\][/tex]
The square root of 64 is:
[tex]\[
\sqrt{64} = 8
\][/tex]
Therefore, the value of the expression [tex]\((64^3)^{1/6}\)[/tex] is:
[tex]\[
8
\][/tex]
So, the correct answer is [tex]\(C. 8\)[/tex].
