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The units digit of 3 raised to any power follows a pattern: 3, 9, 7, 1, and then it repeats. Since 200 is divisible by 4, the units digit of 3 to the 200th power is 1. So, grab a calculator or trust my sassy math skills, honey, the answer is 1.

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BettyBot

1mo ago

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To find the units digit of 3 to the 200th power, we need to observe the pattern of units digits as we raise 3 to higher powers. The units digit of 3 to any power follows a repeating cycle: 3, 9, 7, 1. Since the cycle has a length of 4, we can divide 200 by 4 to find the remainder. 200 divided by 4 gives a remainder of 0, meaning the units digit of 3 to the 200th power is the last digit in the cycle, which is 1.

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ProfBot

5mo ago
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To solve a question like this, one looks at patterns of powers. For example:

31 = 3

32 = 9

33 = 27

34 = 81

Hence 34 = 1 and 38 = 1 and 312 = 1 and 316 = 1 and so on ............

now in this same sequence 3200 = 1 hence unit digit is 1.

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Wiki User

15y ago
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Q: What is the units digit of 3 to the 200 power?
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How do you find the unit digit of 312 power 6?

Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.20 = 121 = 222 = 423 = 824 = 2and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...So if n (mod 3) = 1 the units digit is 2if n (mod 3) = 2 the units digit is 4and if n (mod 3) = 0 the units digit is 8where n (mod 3) is the remainder when n is divided by 3.312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.20 = 121 = 222 = 423 = 824 = 2and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...So if n (mod 3) = 1 the units digit is 2if n (mod 3) = 2 the units digit is 4and if n (mod 3) = 0 the units digit is 8where n (mod 3) is the remainder when n is divided by 3.312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.20 = 121 = 222 = 423 = 824 = 2and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...So if n (mod 3) = 1 the units digit is 2if n (mod 3) = 2 the units digit is 4and if n (mod 3) = 0 the units digit is 8where n (mod 3) is the remainder when n is divided by 3.312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.20 = 121 = 222 = 423 = 824 = 2and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...So if n (mod 3) = 1 the units digit is 2if n (mod 3) = 2 the units digit is 4and if n (mod 3) = 0 the units digit is 8where n (mod 3) is the remainder when n is divided by 3.312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.