What is the ones digit when 6317^458 is written in standard form?

Question

What is the ones digit when 6317^458 is written in standard form?
Any help greatly appreciated!

Please show your work or tell me how you came upon your answer.

6317^458 = 6317 to the power of 458

Answer 1

The pattern for 7s is as follows (watch the final digit):

7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16,807

The last digit repeats 7, 9, 3, 1

So divide 458 by 4, leaves remainder 2.
The final digit is 9.

Answer 2

what you are asking for is 6317^458 mod 10

since
6317 = 7 mod 10 then
6317^458 = 7^458 mod 10

now
7^2 = 49 = 9 mod 10
7^4 = (7^2)^2 = 9^2 = 81 = 1 mod 10
7^458 = (7^4)^114 * 7^2 = 1 * 9 = 9 mod 10

So 6317^458 = 9 mod 10 which is the ones digit. No computer required!

Using congruency it becomes possible for example to say the last 7 digits is 7593609

Answer 3

The ones digit will only depend on the ones digit in 6317, so this comes down to what is the ones digit in 7^458

Now, 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807

So there only are 4 possible values (7,9,3,1)
458 mod 4 = 2 so the ones digit will be the same as 7^2 or 9

Answer 4

The only part of 6317 that effects the ones digit in 6317^n is the the 7.

6317^1 has a one's digit of 7
6317^2 has a one's digit of 9
6317^3 has a one's digit of 3
6317^4 has a one's digit of 1

It repeats with a sequence length of 4. 458 = 114*4 + 2. This means that:

6317^458 has a one's digit of 9.

Answer 5

6

Answer 6

8 is in the ones line if that is what you're meaning....or are you talking about the position of the ^ position? If that is it that is the thousands positions
it goes from right to left.....ones, tens, hundreds, thousands.....so on

Actually I have no clue what you're talking about....sooo

Answer 7

it's 9 for sure, computers are your friends.

Answer 8

wut?

kaity♥