What is the last digit in the number $7^{7^{7^{7^{7^{7^{7}}}}}}$ $7^(7^(7^(7^(7^(7^7)))))$ ?

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Answer 1 · 2015-03-30T19:56:38

The answer is: $7$ $7$ .

This is because:

$7^{7} = a$ $7^7=a$ it's a number whose last digit is $3$ $3$ .

$a^{7} = b$ $a^7=b$ it's a number whose last digit is $7$ $7$ .

$b^{7} = c$ $b^7=c$ it's a number whose last digit is $3$ $3$ .

$c^{7} = d$ $c^7=d$ it's a number whose last digit is $7$ $7$ .

$d^{7} = e$ $d^7=e$ it's a number whose last digit is $3$ $3$ .

$e^{7} = f$ $e^7=f$ it's a number whose last digit is $7$ $7$ .

What is the last digit in the number 7^(7^(7^(7^(7^(7^7)))))77777777^(7^(7^(7^(7^(7^7))))) ?