why X^0=1
EXPLAIN
thanks

2. Originally Posted by Peacewanters007
why X^0=1
EXPLAIN
thanks
it is an axiom, so it is really by convention for lack of a better word. but, the axiom makes sense. maybe this will help

3. Originally Posted by Jhevon
it is an axiom, so it is really by convention for lack of a better word. but, the axiom makes sense. maybe this will help
As there is a way to derive it using the laws of exponents I wouldn't call it an axiom.

-Dan

4. Originally Posted by topsquark
As there is a way to derive it using the laws of exponents I wouldn't call it an axiom.

-Dan
the site i gave called it an axiom, so i just went along with it.

how would you derive it? the same way the site shows?

5. Well,there is a mathematical prove but I didn't see it here.
a $^b$:a $^b$=a $^b$ $^-$ $^b$=a $^0$
The result of dividing two numbers that are the same is 1,so a $^b$:a $^b$=1 That's why a $^0$=1 but there is a rule when a is 0. 0 $^0$ and 0 $^b$ where b is a negative number aren't defined and it is better to leave them instead writing a number because it can be an error.

6. Basically:

When you divide a number by itself, each with their own exponent, you subtract the exponent (to simplify it) ; example 6^5/6^3 = 6^2 ....

OK, so if you get that, then do: 6^5/6^5 .... It equals 6^0 correct? Because you subtract the exponent 5's to get the exponent zero.
But what does dividing any number by itself give you? IT gives you 1, therefore, a^b/a^b=a^0=1

7. Originally Posted by brainmixer
Well,there is a mathematical prove but I didn't see it here.
a $^b$:a $^b$=a $^b$ $^-$ $^b$=a $^0$
The result of dividing two numbers that are the same is 1,so a $^b$:a $^b$=1 That's why a $^0$=1 but there is a rule when a is 0. 0 $^0$ and 0 $^b$ where b is a negative number aren't defined and it is better to leave them instead writing a number because it can be an error.
Originally Posted by mike_302
Basically:

When you divide a number by itself, each with their own exponent, you subtract the exponent (to simplify it) ; example 6^5/6^3 = 6^2 ....

OK, so if you get that, then do: 6^5/6^5 .... It equals 6^0 correct? Because you subtract the exponent 5's to get the exponent zero.
But what does dividing any number by itself give you? IT gives you 1, therefore, a^b/a^b=a^0=1
yes, i see. i just thought maybe there was something more... elegant

8. Well, I guess if that property (as I have described) had not been discovered or pieced together by someone, then we'd be looking at a^0 similar to the way that we look at a/0 ... With absolute chaos and infinite impossiblity... If you really think about it... So it has to be something simple like this to solve for anything to exponent zero .

9. $0^0$ is really just another way to write $\frac{0}{0}$

$k^0 = k^{n - n} = k^n k^{ - n} = \frac{{k^n }}
{{k^n }} = 1$
, $k \ne 0$

for $k=0$: $\frac{{0^n }}{{0^n }} = \frac{0}{0}$

and we all know that anything divided by 0 is undefined, let alone $\frac{0}{0}$.

10. whatz 4x4

11. is that a joke question orrr? (no offence if it is...)

12. Originally Posted by lil50
whatz 4x4