Q: What is the units digit of 3 to the 84th power?

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it is 3

3 to a power divisible by 4 will have a units digit of 1.The powers of 3 are 3, 9, 27, 81 ... obviously, the next one will have a units digit of 1x3 or 3, the next one will have a units digit of 3x3 or 9, the next one will have a units digit of 7 (because 9x3 is 27), the next one will have a units digit of 1 (because 7x3 is 21), and then the cycle starts over with a units digit of 3 again.

The units digit of 20132013 is the same as the units digit of 32013. The units digit of 34 = units digit of 81 = 1 So units digit of 32013 = 32012+1 = 34*503+1 = 34*503 *31 = 1503*3 = 3

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.

6308 6321

Related questions

Power 2: units digit 9. Multiply by 49 again to get power 4: units digit 1. So every 4th power gives units digit 1. So 16th power has units digit 1, so the previous power, the 15th must have units digit 3.

3

it is 3

3 to a power divisible by 4 will have a units digit of 1.The powers of 3 are 3, 9, 27, 81 ... obviously, the next one will have a units digit of 1x3 or 3, the next one will have a units digit of 3x3 or 9, the next one will have a units digit of 7 (because 9x3 is 27), the next one will have a units digit of 1 (because 7x3 is 21), and then the cycle starts over with a units digit of 3 again.

The units digit of 20132013 is the same as the units digit of 32013. The units digit of 34 = units digit of 81 = 1 So units digit of 32013 = 32012+1 = 34*503+1 = 34*503 *31 = 1503*3 = 3

1

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.

I guess you mean what's the units digit of 32011. It is 7. To work this out, see how the units digit of 3n changes; it goes: 3, 9, 7, 1, 3, 9, 7, 1, ... (only the first 8 powers are shown) repeating the same sequence of 4 digits. So if we find the remainder of 2011 divided by 4, it will tell us which of the four numbers (3, 9, 7, 1) will be the units digit of 32011: 2011 ÷ 4 ⇒ remainder 3, so the 3rd digit is the required digit: 7. (If there had been no remainder, then the 4th digit, namely 1, would have been the required value.)

3

6308 6321

1ExplanationNote the following:31=332=933=2734=8135=24336=72937=218738=6561You will see that the units digit of the powers of three cycles through the following: 3, 9, 7, 1. 3 raised to a multiple of 4 has 1 as the units digit. Because 2008 is a multiple of 4, 32008 has 1 in the units digit (and is thus the remainder when that number is divided by 5).

The units digit of any number is the number in the ones position. For example, the units digit of 123 is 3; 2324 is 4; and 87321 is one. The reason the answer is 5 for 5 raised to any positive integer is because 5 will always be in the units position. For example, 52 = 25; 53 = 125; 54 = 625; and so on.