Find the last digit of $\displaystyle 73^{75^{64^{76}}}$
the last digit is $\displaystyle 3$.
Explanation:
Last digit in $\displaystyle 64^{76}$ is 6.
now, $\displaystyle 75^n$ has last two digits 25 if n is even, and last two digits are 75 if n is odd.
Hence, $\displaystyle 75^{64^{76}}$ has last two digits 25.