Let's simplify the expression step by step:
The given expression is:
\[ -15 + \frac{4}{5}(15e^{-10}) - 10e \]
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Calculate \(\frac{4}{5}(15e^{-10})\): \[ \frac{4}{5} \times 15e^{-10} = \frac{60}{5}e^{-10} = 12e^{-10} \]
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Substitute back into the expression: \[ -15 + 12e^{-10} - 10e \]
Since there are no like terms here, we cannot combine \(12e^{-10}\) and \(-10e\) further.
Next, we can rearrange the expression for clarity (though this does not change its value):
\[ 12e^{-10} - 10e - 15 \]
Since there are no further simplifications, we leave it as:
\[ -15 + 12e^{-10} - 10e \]
- Identify which of the options matches if simplified appropriately:
- The expression does not simplify neatly to the forms given in your options involving \(e^{-23}\) or \(e^{23}\).
- Therefore, none of the options provided match the simplified form of the expression directly.
If we needed to decide based solely on form and possible mathematical errors regarding interpreting exponents or simplifications, none match closely, but if \(e^{-10}\) approximated in terms of \(e^{-23}\) via a context being unclear, one could mistakenly interpret results differently.
Thus, from what was calculated, the expression reduces to:
\[ 12e^{-10} - 10e - 15 \]
And no option given corresponds correctly to that expression. If further provided context reveals correct interpretation of the terms, please clarify.