A tower of powers is worked out from the TOP downwards, so $3^3$³ means 3 raised to the power $3^3$. What is the last digit of $3^3$³?

Start at the top: $3^3=27$, so the tower is $3^{27}=7625597484987$. The last digits of the powers of 3 run 3, 9, 7, 1 and then repeat every 4 steps. Since $27=4\times 6+3$, the last digit is the third entry of the cycle, namely 7. The trap is 3: reading the tower from the bottom instead gives $(3^3{)}^3=3^9$, and $9=4\times 2+1$ lands back on the first entry, 3.