The coefficient of $x^{8}$ in the expansion of $e^{3 x}$ is

\frac{3^{7}}{7!}

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\frac{3^{8}}{8!}

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\frac{3^{9}}{9!}

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3^{8}

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Solution

The correct option is D $\frac{3^{8}}{8!}$
General term in the expansion of $e^{x}$ is $\frac{x^{n}}{n!}$
So, the general term in the expansion of $e^{3 x}$ is $\frac{{(3 x)}^{n}}{n!}$
Coefficient of $x^{8}$ in the expansion of $e^{3 x}$ is $\frac{3^{8}}{8!}$

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