Answer: -0.155
Step-by-step explanation: The missing exponent in the equation $500 s^{\text{?}} = 175$ can be found by rearranging the equation and solving for the unknown exponent. To do this, divide both sides of the equation by 500. Now, we can simplify the right side of the equation. To find the value of the exponent, we can take the logarithm of both sides of the equation. However, if you don't have prior knowledge of logarithms, you can use a calculator or estimate the answer. Using a calculator, you can take the logarithm of $\frac{7}{20}$ to the base 10. The logarithm of $\frac{7}{20}$ to the base 10 is approximately -0.155. Therefore, the missing exponent in the equation $500 s^{\text{?}} = 175$ is approximately -0.155.