Multiply. \[ -\frac{3}{5} \cdot \frac{1}{8} \] Write your answer in simplest form.

Step 1 ：Given the problem to solve is \(-\frac{3}{5} \cdot \frac{1}{8}\).

Step 2 ：The rule for multiplying fractions is to multiply the numerators (the top numbers) together to get the new numerator, and multiply the denominators (the bottom numbers) together to get the new denominator.

Step 3 ：The sign of the result is determined by the signs of the fractions being multiplied. In this case, one fraction is negative and the other is positive, so the result will be negative.

Step 4 ：Let's multiply the numerators: \(-3 \cdot 1 = -3\) and the denominators: \(5 \cdot 8 = 40\).

Step 5 ：So, the result of the multiplication is \(-\frac{3}{40}\).

Step 6 ：This fraction is already in simplest form, as the numerator and denominator have no common factors other than 1.

Step 7 ：Final Answer: \(\boxed{-\frac{3}{40}}\)