Predicting how long the result of a permutation

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We're calculating the result of a 'tweaked' Birthday Problem, but when we're calculating, we stumped by a very nasty permutation.

$$10^{576}P_{10^{16}}$$

Which, make us stop working at the number, and call the day.

The formula of the permutation that we understand is:

$$\frac{10^{576}!}{10^{16}!}$$

Is there anyway how do at least 'predict' the length of the number? We already give up on knowing the result, so we just wonder of the massiveness of the number.

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The number of digits would be about $575* 10^{576}$. The $10^{16}$ wouldn't even make a dent in that.

On the other hand, I think $10^{576}P_{10^{16}}$ is the product of $10^{16}$ numbers, all very close to $10^{576}$. That would be $$(10^{576})^{10^{16}}$$ which has $5760000000000000000$ digits.