## anonymous one year ago any thing power zero the answer is 1.this is why any thing behind that? i no need proof i need its physics.

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1. UsukiDoll

The zero exponent rule basically says that any base with an exponent of zero is equal to one. For example: $\LARGE x^0=1$

2. Owlcoffee

It is quite simple, you start with any base to the power of zero: $a^0$ but any number operated by the opposite is equal to zero so I can replace it with n-n=0: $a^0 = a^{n-n}$ But, the sustraction of the exponents is pretty much the division of the bases with the same exponents: $\frac{ a^n }{ a^n }$ And something divided by itself is "1", so therefore: $\frac{ a^n }{ a^n }=1$ $a^0 =1$

3. UnkleRhaukus

NB: $$0^0\neq1$$

4. anonymous

i know this result but i want to know its physics

5. Owlcoffee

By "physics" you mean the way to apply it and the possible scenarios?

6. UsukiDoll

^ I think so... if not then I have no idea what's going on besides giving that definition

7. anonymous

yes why this phenomena happened

8. UsukiDoll

what! That's impossible! We have to go way far back.. it's just a rule that's written in stone and everyone must follow it.

9. anonymous

Nice (: didn't know that before

10. Owlcoffee

It's a property that came with the definition of "exponent" in mathematics. You see, Mathematics has it's bases on what are called the "axioms" which are "theorems" that do not have any proof because they are considered "true". They are indeed the definition that form the bases of mathematics and from them, derived all the theorems that we know today. The exponents were defined pretty much as: $\prod_{i=1}^{i=n}a_i = a_1.a_2.a_3...a_n=a^n$ With the condition that the a_1 to a_n are all the same constant. And from that definition, which was studied exhaustedly derived the theorems or property of the exponents you use in your algebra classes.

11. Empty

@Yasirist This is an excellent question! If I write $$x^2$$ that 2 means I am really multiplying a number x by itself two times, like this $$x*x$$ which you well know! So we have nice things such as let's say we want to multiply these numbers together: $x^2*x^3$ We might not know, do we multiply or add the 2 and 3 together? Well one simple way to find out it to write it all out by what the 2 and 3 really mean, just multiply x by itself twice and multiply x by itself 3 times. $x^2 *x^3 = (x*x)*(x*x*x) = x*x*x*x*x = x^5$ Ahhh so we see that the rule must be adding! $x^2*x^3=x^{2+3}=x^5$ We can write this more generally as: $x^n*x^m=x^{n+m}$ What if now we say m=0 in this formula? $x^n*x^0 = x^{n+0}$ We see that this is really just: $x^n*x^0=x^n$ So we must accept that $$x^0=1$$, because we know $$x^n*1=x^n$$. But this is still unsatisfying to us! What does this mean? We can see that it must be true, but why is it so?! Let us again think back to our definitions. We know that $$x^2$$ just means x multiplied by itself twice. What about $$x^1$$? This is just x multiplied by itself 1 time, which seems weird to say, but we can probably accept that it just means one x. Now how about $$x^0$$? This means x multiplied no times! That means there aren't even any x's there. You will say, "This too is unsatisfying!" and I agree with you. Maybe we can't understand such a thing from this perspective? By analogy with physics, not even Einstein understood gravity! He only ever was able to describe how it behaves by imagining gravity as a curvature of space. Maybe at the end of the day, nothing is truly understandable? Or maybe we just haven't gotten to the bottom of it yet.