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To find the last digit of 3^1234, we can use the following steps:
1. Observe the pattern of the last digit of powers of 3:
3^1 = 3 (last digit is 3)
3^2 = 9 (last digit is 9)
3^3 = 27 (last digit is 7)
3^4 = 81 (last digit is 1)
2. The pattern repeats in a cycle of 4 digits: 3, 9, 7, 1.
3. To find the last digit of 3^1234, we can divide 1234 by 4 to find the number of complete cycles, and then look at the remainder to determine the last digit.
4. 1234 ÷ 4 = 308 with a remainder of 2.
5. Since the remainder is 2, the last digit of 3^1234 will be the same as the last digit of 3^2, which is 9.
Therefore, the last digit of 3^1234 is 9.
Answer: The last digit of (3^{1234}) is 1.
Step-by-step explanation: To determine this, we can observe the pattern of the units digit of powers of 3:
The units digit repeats in cycles of 4: 3, 9, 7, 1. Since 1234 is divisible by 4 (1234 ÷ 4 = 308 with no remainder), the units digit of (3^{1234}) is the last digit in the cycle, which is 1.
Hope you solve your problems :)