# Question #4b94f

Nov 6, 2016

Perhaps someone else can add a more in depth explanation

#### Explanation:

This is a subject that is argued about a lot.

$\textcolor{b l u e}{\text{View point 1:}}$

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

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$\textcolor{b l u e}{\text{View point 2: }}$

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

${0}^{0} \ne 1$ 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 $\frac{0}{0}$ and to have 0 as the denominator makes the whole thing 'undefined'.

This in turn makes ${0}^{0}$ undefined.

$\textcolor{p u r p \le}{\text{Bit of a dilemma, isn't it!}}$