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Possible Duplicate:
The last two digits of $9^{9^9}$

How to find the last two digits of $9^{9^{9^9}}$ (a power tower of 4 $9$'s) ?

Is there any special approach to these kind of problems?

  • 0
    Hint: the last digit is the number mod $10$,$81 mod 10=1$2012-07-07
  • 3
    You can follow the approach in [this problem](http://math.stackexchange.com/q/65454/264). Is this sufficiently similar to be a duplicate?2012-07-07
  • 2
    @Zev, methinks yes.2012-07-07
  • 0
    Yes, enough @ZevChonoles2012-07-07
  • 1
    Also some discussion at http://math.stackexchange.com/questions/166083/last-few-digits-of-nnn-cdot-cdot-cdotn/166133#1661332012-07-07
  • 0
    Related: [How do I compute $a^b\,\bmod c$ by hand?](http://math.stackexchange.com/questions/81228)2015-08-20

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