Question

Question #4b94f

Answer 1

Perhaps someone else can add a more in depth explanation

Explanation:

This is a subject that is argued about a lot.

`color(blue)("View point 1:")`

Any number raised to the power of zero is 1.
Hence: `0^0=1`

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`color(blue)("View point 2: ")`

Some argue that 0 is not a number it is a placeholder so

`0^0!=1` as `0^0` is 'undefined'
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The problem stems from the following:

Consider the example `3^2/3^2 = 3^(2-2)=3^0=1` which is true.

However to end up with `0^0` we would need to have

`0^x/0^x = 0^(x-x)=0^0`

However `0^x=0` so we have `0/0` and to have 0 as the denominator makes the whole thing 'undefined'.

This in turn makes `0^0` undefined.

`color(purple)("Bit of a dilemma, isn't it!")`