Makakuha ng mabilis at malinaw na mga sagot sa IDNStudy.com. Magtanong ng anumang bagay at makatanggap ng kumpleto at eksaktong sagot mula sa aming komunidad ng mga propesyonal.
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 :)