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anonymous

  • 4 years ago

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

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  1. anonymous
    • 4 years ago
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    should be 1

  2. anonymous
    • 4 years ago
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    do you want an explanation?

  3. anonymous
    • 4 years ago
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    Yes please

  4. anonymous
    • 4 years ago
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    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....

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

  6. anonymous
    • 4 years ago
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    Maribor?

  7. anonymous
    • 4 years ago
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    can you show me how you resolved the issue

  8. anonymous
    • 4 years ago
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    I will, but I need to make sure you got what I said above XD

  9. anonymous
    • 4 years ago
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    yes I do

  10. anonymous
    • 4 years ago
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    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.

  11. anonymous
    • 4 years ago
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    OK Thanks for your help

  12. anonymous
    • 4 years ago
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    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.

  13. anonymous
    • 4 years ago
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    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

  14. anonymous
    • 4 years ago
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    Thanks again

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