11 questions linked to/from The last two digits of $9^{9^9}$
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Finding the last two digits of $9^{9^{9^{…{^9}}}}$ (nine 9s) [duplicate]

I'm continuing on my journey learning about modular arithmetic and got confused with this question: Find the last two digits of $9^{9^{9^{…{^9}}}}$ (nine 9s). The phi function is supposed to be used ...
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Find the last two digits of $9^{9^{9}}$ [duplicate]

I want to find the last two digits of $9^{9^9}$ or $9^{81}$. I tried using Euler's theorem but I can't make anything of it. Any hint or a guide? Thanks!
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Clarification needed on finding last two digits of $9^{9^9}$

I stumbled across this problem here. In the answer given by the user Gone, I don't see how he makes use of the second line in the last line. Could someone explain why he calculated $9^{10}$ via ...
How to find the last two digits of $9^{9^{9^9}}$? [duplicate]
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?
How do I compute $a^b\,\bmod c$ by hand?
How do I efficiently compute $a^b\,\bmod c$: When $b$ is huge, for instance $5^{844325}\,\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, ...