What is the rightmost digit preceding the zeros in the value of $30^{30}$?
What is the rightmost digit preceding the zeros in the value of $30^{30}$?
1
3
7
9
Solution
$30^{30} = (10 \times 3)^{30} = 3^{30} \times 10^{30}$. The $10^{30}$ contributes 30 trailing zeros, so the digit just before the zeros is the unit digit of $3^{30}$. The unit digit of powers of 3 has cyclicity 4 (3, 9, 7, 1). Since $30 = 4 \times 7 + 2$, the unit digit of $3^{30}$ is the same as $3^2 = 9$.