To find [tex]\( f(-4) \)[/tex] for the given function [tex]\( f(x) = 2^x \)[/tex], you can follow these steps:
1. Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-4) = 2^{-4}
\][/tex]
2. Simplify the expression [tex]\( 2^{-4} \)[/tex]. Recall that a negative exponent indicates a reciprocal. Thus, [tex]\( 2^{-4} \)[/tex] is the same as [tex]\( \frac{1}{2^4} \)[/tex]:
[tex]\[
2^{-4} = \frac{1}{2^4}
\][/tex]
3. Calculate [tex]\( 2^4 \)[/tex]:
[tex]\[
2^4 = 2 \times 2 \times 2 \times 2 = 16
\][/tex]
4. Substitute [tex]\( 2^4 \)[/tex] back into the reciprocal to get:
[tex]\[
\frac{1}{2^4} = \frac{1}{16}
\][/tex]
So, the value of [tex]\( f(-4) \)[/tex] is [tex]\( \frac{1}{16} \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{1}{16}}
\][/tex]
