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Determine the density function of the maximum of a random sample of size $n$ from an exponential distribution with rate parameter $\eta$

So I don't really know where to start with this, any help appreciated.

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HINT

$$P(\max X_i\le x) = P(X_1\le x,X_2\le x,\ldots,X_n\le x).$$ For most exercises about the maximum of random variables, this is how the solution starts.

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