To simplify the expression involving the functions \( f \) and \( e \) you've given, we first need to clarify the input you provided. It looks like you're asking to simplify a fraction with functions raised to powers.
The expression seems to look like this:
\[ \frac{f^7 e^2 f^4}{f^{11} e^9} \]
If we simplify this step by step:
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Combine the powers of \( f \) in the numerator: \[ f^7 f^4 = f^{7+4} = f^{11} \]
Now the expression becomes: \[ \frac{f^{11} e^2}{f^{11} e^9} \]
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Cancel \( f^{11} \) from the numerator and the denominator: \[ = \frac{e^2}{e^9} \]
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Simplify the powers of \( e \): \[ e^2 / e^9 = e^{2-9} = e^{-7} \]
Thus, the simplified version of the given expression is: \[ e^{-7} \]
If you meant a different expression or format, please clarify!