To evaluate [tex]\(2^{-4}\)[/tex], we should follow a step-by-step approach. Let's break it down.
1. Understand Negative Exponent:
A negative exponent means we need to take the reciprocal of the base raised to the positive of that exponent. In mathematical terms, [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex].
2. Convert the Negative Exponent:
Apply this rule to [tex]\(2^{-4}\)[/tex]:
[tex]\[
2^{-4} = \frac{1}{2^4}
\][/tex]
3. Calculate the Exponentiation:
Calculate [tex]\(2^4\)[/tex] (which means multiplying 2 by itself four times):
[tex]\[
2^4 = 2 \times 2 \times 2 \times 2 = 16
\][/tex]
4. Take the Reciprocal:
Now take the reciprocal of 16:
[tex]\[
\frac{1}{2^4} = \frac{1}{16}
\][/tex]
Thus, the value of [tex]\(2^{-4}\)[/tex] is [tex]\(\frac{1}{16}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(\frac{1}{16}\)[/tex]
