• ThatWeirdGuy1001@lemmy.world
    0·
    1 year ago

    I know I’m bad at math but I don’t understand how 2x0=0 but 2^0=1

    How are they different answers when they’re both essentially multiplying 2 by zero?

    Someone with a bigger brain please explain this

    Edit: I greatly appreciate all the explanations but all they’ve done is solidify the fact that I’ll never be good at math 😭

    • jendrik@discuss.tchncs.de
      0·
      1 year ago

      subtracting one from Exponent means halving (when the base is two):

      2⁴ = 16 2³ = 8 2² = 4 2¹ = 2 2⁰ = 1

      It’s a simple continuation of the pattern and required for mathemarical rules to work.

      • uberrice@feddit.de
        0·
        1 year ago

        This is confidently wrong.

        3^0 is also 1. 2738394728^0 is also 1.

        Edit: just saw that technically you’re correct - sure.

        IF base 2, Exponent reduction equals to halving - dividing by 2.

        For x^y reducing y by one is equal to dividing by x, then we have the proof it always works.

    • Globulart@lemmy.world
      0·
      1 year ago

      This isn’t strictly speaking a proof, but it did help me to accept it as it demonstrates the function that makes it 1.

      2^3 = 2x2x2

      2^2 = 2x2

      (23)/(22) = (2x2x2)/(2x2) = 2

      = 2^(3-2)

      In general terms:

      (xa)/(xb) = x^(a-b)

      If a and b are the same number this is x^0 and obviously (xa)/(xa) is one because anything divided by itself is 1.

      Hope that helps

        • Flumsy@feddit.de
          0·
          1 year ago

          That was pretty complicated, here is a simpler answer I hsve come up with:

          1=(2x2x2)/(2x2x2)=2³/2³=2³⁻³＝2⁰

          If that makes sense to you…