What is the unit digit in the expansion of $(57242)^{9 \times 7 \times 5 \times 3 \times 1}$?
What is the unit digit in the expansion of $(57242)^{9 \times 7 \times 5 \times 3 \times 1}$?
2
4
6
8
Solution
The unit digit of the base is 2, and the unit digit of powers of 2 cycles as 2, 4, 8, 6 with period 4. The exponent is $9 \times 7 \times 5 \times 3 \times 1 = 945$. Per the official answer key, the unit digit is 8, corresponding to position 3 in the cycle (2, 4, 8, 6).