10 is approximately the largest number of objects we can think about simultaneously.

10^10 is approximately the largest number we can count to, perhaps with the aid of tools. The largest number we can write down in base 1 (unary), e.g., tally marks.

10^10^10 is approximately the largest number we can write down its digits in their entirety in base 10 (or in any base higher than 1).

10^10^10^10 is approximately the largest number we can write down in scientific notation, rounded to a small number (less than 10^10) of significant digits.

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