A5. If the number $\left(\left(\left(\left(7^{6}\right)^{5}\right)^{4}\right)^{3}\right)^{2}$ is written out, what is the last digit?
A) 1
B) 3
C) 5
D) 7
E) 9
A5. A) 1 The product of two numbers that end in 1 also ends in 1. Since the last digit of $7^{4}=2401$ is 1, this also holds for any power of $7^{4}$. In particular, the last digit of $\left.\left(\left(\left(7^{6}\right)^{5}\right)^{4}\right)^{3}\right)^{2}=7^{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2}=\left(7^{4}\right)^{180}$ is 1.