To solve the equation
\[ \frac{e^?}{e^{65}} = e^{38}, \]
we can simplify the left side of the equation using the properties of exponents. Specifically, we can use the rule that states \(\frac{a^m}{a^n} = a^{m-n}\). Applying this rule here gives us:
\[ e^{? - 65} = e^{38}. \]
Since the bases (which are both \(e\)) are the same, we can set the exponents equal to each other:
\[ ? - 65 = 38. \]
To find \(?\), we can solve for it by isolating it on one side of the equation:
\[ ? = 38 + 65. \]
Calculating this:
\[ ? = 103. \]
Thus, the missing exponent is
\[ \boxed{103}. \]
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