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    Can someone please explain this problem.

    Module 5 Day 3 Your Turn Part 3
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    • N
      neatlobster M5 last edited by debbie

      Module 5 Day 3 Your Turn Part 3 Mini-Question Solution

      It says that this number is odd, when it is even because 8^7^6^5 and so on can be expressed as 8^(7!), and we know that even*even=even.

      v4913 1 Reply Last reply Reply Quote 4
      • v4913
        v4913 MOD M0 M1 M2 M3 M4 M5 @neatlobster last edited by

        Very close! It would only be equal to 8^(7!) if there were parentheses around each term like this:
        Screenshot from 2021-01-20 09-37-40.png
        If there are no parentheses, the powers cannot be multiplied, and so it equals this:
        Screenshot from 2021-01-20 09-28-48.png
        Since the exponent on the 8 is a power of 7, which is odd, the answer is equal to 8^{1} mod 9.

        N 1 Reply Last reply Reply Quote 6
        • mathnerd_101
          mathnerd_101 M3 last edited by

          @v4913 said in Can someone please explain this problem.:

          Very close! It would only be equal to 8^(7!) if there were parentheses around each term like this:
          Screenshot from 2021-01-20 09-37-40.png
          If there are no parentheses, the powers cannot be multiplied, and so it equals this:
          Screenshot from 2021-01-20 09-28-48.png
          Since the exponent on the 8 is a power of 7, which is odd, the answer is equal to 8^{1} mod 9.

          o pro v4913 post o

          1 Reply Last reply Reply Quote 3
          • N
            neatlobster M5 @v4913 last edited by

            @v4913 Ok, thanks! I also have another question about this problem. When it is odd, why is the answer -1 mod 9?

            debbie audrey v4913 3 Replies Last reply Reply Quote 3
            • debbie
              debbie ADMIN M0★ M1 M5 @neatlobster last edited by

              @neatlobster @v4913 Thank you 🙂

              1 Reply Last reply Reply Quote 2
              • audrey
                audrey MOD @neatlobster last edited by

                This post is deleted!
                1 Reply Last reply Reply Quote 0
                • v4913
                  v4913 MOD M0 M1 M2 M3 M4 M5 @neatlobster last edited by

                  @neatlobster Good question! Since 8 = -1 mod 9, and the powers of -1 go -1, 1, -1, 1, etc, all (-1)^{even} = 1 mod 9 and all (-1)^{odd} = -1 mod 9. Since we are talking about modulos, and 8 is the same as -1 mod 9, this means (8)^{even} = 1 mod 9, and (8)^{odd} = -1 mod 9.

                  1 Reply Last reply Reply Quote 2
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