What is the last digit of $2023^{2024^{2025}}$?
We notice that $3^{2} \equiv 9 \equiv -1(\bmod 10)$, so $3^{4} \equiv 1(\bmod 10)$. Moreover, $2024^{2025}$ is a multiple of 4, so we have once again $2023^{2024^{2025}} \equiv 1(\bmod 10)$.