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

Mar 30, 2015

The answer is: $7$.

This is because:

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

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

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

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

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

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