anonymous
  • anonymous
What are the positive residual obtained when (17 ^ 15 +8 ^ 25) ^ 10 divided by 10?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
should be 1
anonymous
  • anonymous
do you want an explanation?
anonymous
  • anonymous
Yes please

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anonymous
  • anonymous
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....
anonymous
  • anonymous
like....225 divided by 10...the residue would be 5. 332 divided by 10, the residual would be 2. Do you get that??
anonymous
  • anonymous
Maribor?
anonymous
  • anonymous
can you show me how you resolved the issue
anonymous
  • anonymous
I will, but I need to make sure you got what I said above XD
anonymous
  • anonymous
yes I do
anonymous
  • anonymous
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.
anonymous
  • anonymous
OK Thanks for your help
anonymous
  • anonymous
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.
anonymous
  • anonymous
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
anonymous
  • anonymous
Thanks again

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