why X^0=1
EXPLAIN
thanks
Well,there is a mathematical prove but I didn't see it here.
a$\displaystyle ^b$:a$\displaystyle ^b$=a$\displaystyle ^b$$\displaystyle ^-$$\displaystyle ^b$=a$\displaystyle ^0$
The result of dividing two numbers that are the same is 1,so a$\displaystyle ^b$:a$\displaystyle ^b$=1 That's why a$\displaystyle ^0$=1 but there is a rule when a is 0. 0$\displaystyle ^0$ and 0$\displaystyle ^b$ 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.
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
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 .
$\displaystyle 0^0 $ is really just another way to write $\displaystyle \frac{0}{0}$
$\displaystyle k^0 = k^{n - n} = k^n k^{ - n} = \frac{{k^n }}
{{k^n }} = 1$, $\displaystyle k \ne 0$
for $\displaystyle k=0$: $\displaystyle \frac{{0^n }}{{0^n }} = \frac{0}{0}$
and we all know that anything divided by 0 is undefined, let alone $\displaystyle \frac{0}{0}$.