I do not understand!!! Can some one please explain it to me.
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I do not understand!!! Can some one please explain it to me.
I am sorry, but this is a bit too advanced for me, mind explaining what e ^ ln(x)y means?
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 $\displaystyle 1=\frac{x^1}{x^1}=x^{1-1}=x^0$
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 :)
Only if $\displaystyle x\ne 0$.
One can see here how complicated this question has become.
I didn't want to open up that can of worms.
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 $\displaystyle \displaystyle \begin{align*} a \neq 0 \end{align*}$.
its only by definition.... no need for ..proofs...they do not mean anything...
Whoops. Too fast. Already done by Plato and Romsek (integer exponents). Missed it. Oh well, I'm not the only one.
My apologies.