To solve for the missing exponent in the equation \( s^{500} s^\text{?} = s^{175} \), we can use the properties of exponents. The property that applies here is \( s^a s^b = s^{a+b} \).
Using that property, we can rewrite the left side of the equation:
\[ s^{500} s^\text{?} = s^{500 + \text{?}} \]
Now we can set the left side equal to the right side:
\[ s^{500 + \text{?}} = s^{175} \]
Since the bases (s) are the same, we can equate the exponents:
\[ 500 + \text{?} = 175 \]
To find the value of the missing exponent (?), we can rearrange the equation:
\[ \text{?} = 175 - 500 \]
Calculating that gives:
\[ \text{?} = -325 \]
Thus, the missing exponent is:
\[ \boxed{-325} \]
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