To find out how much chili powder Karl should use, we need to calculate half of the amount called for in the recipe, which is \(\frac{3}{8}\) cup.
To find half of \(\frac{3}{8}\), we can multiply it by \(\frac{1}{2}\):
\[ \frac{3}{8} \times \frac{1}{2} = \frac{3 \times 1}{8 \times 2} = \frac{3}{16} \]
Therefore, Karl should use \(\frac{3}{16}\) of a cup of chili powder.
The correct answer is \(\frac{3}{16}\) of a cup.