Discussion

Find the unit digit of \(7^{7^{7}}\).

Answer: B

To find the unit digit of \(7^{7^7}\), we need to find the remainder of the power \(7^7\) when divided by the cycle length of 7, which is 4. So we need to find \(7^7 \pmod 4\). We can write 7 as \(8-1\). So, \(7 \equiv -1 \pmod 4\). Then \(7^7 \equiv (-1)^7 = -1 \equiv 3 \pmod 4\). The remainder of the power is 3. We need the 3rd unit digit in the cycle of 7 (7, 9, 3, 1), which is 3.