1 23 23 23 23,2011What is the single digit of the product of 23 phases?

Instead of multiplying 2011 23s, you can look at multiplying 2011 3s, and the product of their single digits is the same.

Let's look at 1 3 single digits is 3

2 3s multiplied = 3 3 = 9 The single digit is 9

3 3 multiplied = 3 3 3 = 27 The single digit is 7

4 3 multiplication = 3 3 3 3 = 81 single digit numbers are 15 3 3 multiplication = 3 3 3 3 3 = 243 single digits are 3 The law is 3 9 7 1 four numbers cycle.

So what is the single digit of 3 multiplied in 2011?

Put 2011 4 = 502....3

The remainder is the number of 2011 23 multiplied by the single digit is 3 9 7 1 The remainder is 3 then 2011 23 multiplied by 7 digits is 7

If it helps you, I hope thank you.

I use the method of number theory to resolve, for reference:

Both (23) 2011 is in the single digits.

23)^2011≡？(mod10)

10)=4, (23)^4≡1(mod10), 2011=4*502+3

23) 2011 (23) (4*502+3) (23) 3 7 (mod10), so 23) The single digit of 2011 is 7

The single digits are 9, 7, 1, 3 cycles.

The unit digit of the 2011 23 multiplied is 1

202 3s multiplied = 3 202=

It can be seen that the single digit of each Cha Zheng power of 3 is 3971 cycle.

202=50x4+2.Therefore, the number on the unvertical single digit is (9).

Summary. He's such a cycle, there is a law on single digits, 97134 number 1 cycle, so 45 13 multiplied is 45 4 equals 11 and 1, so this number should be a single digit, it should be 9.

What is the single digit of the product of 13 13 13 13 multiplied by 13.

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Dear, the single digit of this 13 multiplied is 9 7 1 3 9 7 1 3

He is such a cycle, there is a law on single digits, 97134 number 1 cycle, so 45 13 multiplication is 45 4 and other things are 11 and 1, so this number should be a single digit, should be 9 acres.

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How is it calculated? Some don't understand.

Dear, the number of this calculation is very large, you can only count the single digit, because the search is wide for it only to find a single digit, because the number of single digits is multiplied, it is a circular law, so it is said that Shiliang it 45 13 multiplication, it is in accordance with the above law, you just need to remember this.

First of all, let me explain that the previous answer was because he misunderstood the meaning, he thought it was 2014 3, and the fact should be 2014 to the power of 2,014, and the mantissa of 3 multiplied by 3 is regular, respectively...It can be seen that it is a cycle of 4 digits, so 2014 4 = 503 surplus 2, so the single digit is 7, your praise is the motivation for me to continue!

1 x 3 in the single digit: 3

2 x 3's digits: 9

3 x 3's in the single digit: 7

4 x 3's in the single digits: 1

5 3's scumbags: 3

6 x 3's: 9

7 x 3's in the single digits: 7

8 auspicious units of 3s: 1

4 is a reincarnation.

2011 4 = 502 remainder 3

So the single digit of 2011 multiplied by 3 is 7,4,3=3 and so on (3,9,7,1),(3,9,7,1).2011/4=502...3 So the final answer is 7,2, and the number of regular strings is cyclical 3 9 7 1 3 9 7 1 3.

A group of four numbers Therefore, the single digit is 7,1,3,9,7,1, these 4 numbers are a reincarnation, and the 2011th is 2011 4=502....3, is 7, 1, and a 3 is 3

2 is 9 3 27

4 x 81 5 x 243

So the law is that the single digit cycles with 3, 9, 7, 1.

The single digit of the product has the following characteristics of guessing the orange Cycle in the acre, starting from the first 3 every 4 cycles, so 202 4 = 50....2, so the single digit of the result obtained is 9

Answer: The number of the resulting spikes is 9

Therefore, d

3 3 3 3 3 3 = 243 is 3

3 6 for 9

3 7 for 7

3 8 for 1

Therefore, the single digit of 3 2006 = 3 (4 501+2) = (3 4) 501 981 is 1, so the single digit of 3 2006 is 9

Because this question only asks for single digits, and thousands, hundreds, and tens of digits will not affect the single digits.

So just look at the number of limbs in the single position.

3x3=9 9x3=27 7x3=21 1x3=3 can get 5 for a cycle, and 2000=400x5, so the answer slip is 3