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28 July, 00:44

How do you prove any number to the zero power is 1? Like why is any number to the zero power one?

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  1. 28 July, 02:18
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    Step-by-step explanation:

    It's a matter of being consistent in a pattern:

    Let a be a number. If a^ (-3) is the first number, it's equal to 1 / a^3.

    Next:

    1 / a^2

    1 / a^1

    ? To fit into this pattern, a^0 must equal 1.

    a^1

    a^2

    a^3

    and so on.

    Try this same exercise with a = 2:

    2^ (-2) = 1/4

    2^ (-1) = 1/2

    ? This number has to be 1 to fit the pattern. 2^0 = 1. Note that each

    term is 2x the previous term: 2 (1/4) = 1/2; 2 (1/2) = 1; 2 (1) = 2; 2 (2) = 4,

    and so on. Again, 2^0 must = 1 to fit into this sequence.

    2^1 = 2

    2^2 = 4
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