• GigglyBobble@kbin.social
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    1 year ago

    2^0 isn’t multiplying by zero. Considering this law: 2^a / 2^b = 2^(a-b)
    it’s obvious why 2^0 = 1
    If a=b you’re dividing by the same number resulting in 1.

    Unfortunately, I cannot explain/prove the first law though.

    • zalgotext@sh.itjust.works
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      1 year ago

      The first rule is just simple division:

      (2x2x2x2) / (2x2) =

      (2/2) * (2/2) * 2 * 2=

      1 * 1 * 2 * 2 =

      2 * 2 =

      4

      Writing in terms of powers:

      (2^4) / (2^2) =

      (2^(4-2)) =

      (2^2) =

      4

      The two bottom 2’s “cancel out” (really they just divide into one another to make 1’s) two of the top 2’s and you’re left with two top twos.