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There is a proof, but it is rather complicated to appear here. An intuitive way of thinking about it is to write a list of powers for any number (we'll use 2):

Power: 1 2 3 4 5

Result: 2 4 8 16 32

What you can note is that the next power is calculated by multiplying the current power by the 2; so 25 = 32, 26 = (32 x 2) = 64.

Working the other way, you can generate the previous power by dividing by 2; 25 = 32, 24 = (32 / 2) = 16.

Using this last technique, 21 = 2, 20 = (2/2) = 1.

It should be easy to see that this is true for any number x1 = x and x0 = (x/x) = 1.

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15y ago

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