I do not understand!!! Can some one please explain it to me.

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- Dec 5th 2013, 03:24 PM #1

- Dec 5th 2013, 03:28 PM #2

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- Dec 5th 2013, 03:34 PM #3

- Dec 5th 2013, 03:40 PM #4
## Re: why is x^0 = 1?

Here is a less obscure reason.

First of all, there is some debate about what $\displaystyle 0^0$ could mean.

So let's say that $\displaystyle x\ne 0~.$

Then $\displaystyle \frac{x}{x}=1$ but that means $\displaystyle \frac{x^1}{x^1}=1$.

So by the laws of exponents we have $\displaystyle 1=\frac{x^1}{x^1}=x^{1-1}=x^0$

- Dec 5th 2013, 03:41 PM #5

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- Dec 5th 2013, 04:34 PM #6

- Dec 5th 2013, 05:00 PM #7

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- Dec 5th 2013, 05:19 PM #8

- Dec 5th 2013, 05:37 PM #9

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- Dec 5th 2013, 05:58 PM #10
## Re: why is x^0 = 1?

From the index law $\displaystyle \displaystyle \begin{align*} \frac{a^m}{a^n} = a^{m - n} \end{align*}$, in the case where $\displaystyle \displaystyle \begin{align*} m = n \end{align*}$ we have

$\displaystyle \displaystyle \begin{align*} LHS &= \frac{a^m}{a^n} \\ &= \frac{a^m}{a^m} \\ &= 1 \end{align*}$

but we also have

$\displaystyle \displaystyle \begin{align*} RHS &= a^{m - n} \\ &= a^{m - m} \\ &= a^0 \end{align*}$

Thus $\displaystyle \displaystyle \begin{align*} a^0 = 1 \end{align*}$.

This is of course provided that $\displaystyle \displaystyle \begin{align*} a \neq 0 \end{align*}$.

- Dec 7th 2013, 09:11 AM #11

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- Dec 7th 2013, 09:41 AM #12

- Dec 7th 2013, 12:16 PM #13

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- Dec 7th 2013, 08:13 PM #14

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## Re: why is x^0 = 1?

- Dec 8th 2013, 01:35 AM #15
## Re: why is x^0 = 1?