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

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- Dec 5th 2013, 03:24 PMsakonpure6why is x^0 = 1?
I do not understand!!! Can some one please explain it to me.

- Dec 5th 2013, 03:28 PMromsekRe: why is x^0 = 1?
- Dec 5th 2013, 03:34 PMsakonpure6Re: why is x^0 = 1?
I am sorry, but this is a bit too advanced for me, mind explaining what e ^ ln(x)y means?

- Dec 5th 2013, 03:40 PMPlatoRe: 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 PMromsekRe: why is x^0 = 1?
- Dec 5th 2013, 04:34 PMsakonpure6Re: why is x^0 = 1?
How did we conclude x^0 dont we generaly add the exponents when multiplying them? And how did you conclude the1? I really appreciate it.

@Plato, Ooohh, I see. Thanks :) - Dec 5th 2013, 05:00 PMromsekRe: why is x^0 = 1?
- Dec 5th 2013, 05:19 PMPlatoRe: why is x^0 = 1?
Only if $\displaystyle x\ne 0$.

One can see here how complicated this question has become. - Dec 5th 2013, 05:37 PMromsekRe: why is x^0 = 1?
I didn't want to open up that can of worms.

- Dec 5th 2013, 05:58 PMProve ItRe: 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 AMMINOANMANRe: why is x^0 = 1?
its only by definition.... no need for ..proofs...they do not mean anything...

- Dec 7th 2013, 09:41 AMPlatoRe: why is x^0 = 1?
- Dec 7th 2013, 12:16 PMHartlwRe: why is x^0 = 1?
Whoops. Too fast. Already done by Plato and Romsek (integer exponents). Missed it. Oh well, I'm not the only one.

My apologies. - Dec 7th 2013, 08:13 PMMINOANMANRe: why is x^0 = 1?
- Dec 8th 2013, 01:35 AMtopsquarkRe: why is x^0 = 1?