1. ## Last digit

Find the last digit of $73^{75^{64^{76}}}$

2. the last digit is $3$.

Explanation:
Last digit in $64^{76}$ is 6.

now, $75^n$ has last two digits 25 if n is even, and last two digits are 75 if n is odd.

Hence, $75^{64^{76}}$ has last two digits 25.

3. And to conclude, you have to use the fact that $73^{\varphi(10)}=73^4 \equiv 1 (\bmod 10)$