Question

What are the positive residual obtained when (17 ^ 15 +8 ^ 25) ^ 10 divided by 10?

Answer 1

should be 1

Answer 2

do you want an explanation?

Answer 3

Yes please

Answer 4

ok :)
so, to start off, we need to understand that the positive residual is like a remainder...so anything that is a remainder after being divided by 10 is just the number that is in the one's digit....

Answer 5

like....225 divided by 10...the residue would be 5. 332 divided by 10, the residual would be 2. Do you get that??

Answer 6

Maribor?

Answer 7

can you
show me how you resolved the issue

Answer 8

I will, but I need to make sure you got what I said above XD

Answer 9

yes I do

Answer 10

ok, good :)
so that means you only need to concentrate on the last digit of every number.
17^1=17 last digit is 7
17^2=289 last digit is 9
17^3=4913 last digit is 3
17^4=83521 last digit is 1
17^5=1419857 last digit is 7

So, by this, we can see that this sequence of 7931 is going to loop every four exponents.
In the question above, 17 is raised to the 15 th power. Therefore,
7 9 3 1 7 9 3 1 7 9 3 1 7 9 3
The 15th number ends with 3.

Answer 11

OK Thanks for your help

Answer 12

Now, taking the same pattern with 8:
8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8. The last number raised to the 25th power is 8.

Answer 13

add these last digits up and you should get 1. 1^10 is 1 so the remainder of this equation is 1. Sorry for the lengthy explanation XD

Answer 14

Thanks again