• @Globulart@lemmy.world
    15•9 months 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
        3•9 months 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…

      • @Globulart@lemmy.world
        3•9 months ago

        2^(a-b) = (2a)/(2b)

        You can see this in the example above but perhaps it’s better to use different powers to make things a bit clearer.

        2^5=2x2x2x2x2

        2^3=2x2x2

        (25)/(23)=(2x2x2x2x2)/(2x2x2)

        You can cancel 3 of the 2s from the top and bottom of the fraction to be left with 2x2, or 2^2.

        I.e. (25)/(23)=2^2

        The quicker way to calculate this is doing 2^(5-3) which when you resolve the bracket is obviously just 2^2 or 2x2.

        If both numbers in the bracket are the same the bracket will always resolve to 0, which is the same as saying a number divided by itself, any number divided by itself is one so it follows that any number to the power 0 is also 1 (because it’s essentially exactly the same calculation).