Why is it so that x^0, no matter what the x is, is always equal to 1?
(is it just rule, or there is a logic behind it?)

Question

Why is it so that x^0, no matter what the x is, is always equal to 1?
(is it just rule, or there is a logic behind it?)

hartnn · Answer

except for x=0 ofcourse.

hartnn · Answer

you know whats an identity for multiplication ?

hartnn · Answer

like identity for addition is 0
anything +0 = anything.

solomonzelman · Answer

I don't think so, 0^0....actually not sure, hold.....

solomonzelman · Answer

yep 0^0 is 1, check on google calc.

hartnn · Answer

google calc is incorrect. http://www.wolframalpha.com/input/?i=0%5E0&dataset=

solomonzelman · Answer

Weird isn't it, but......
Anyway, is there a logic behind that or it is just an explainable rule.

solomonzelman · Answer

First time I see google calc is incorrect... let me check your....

solomonzelman · Answer

it says indeterminate, is that no solution?

hartnn · Answer

x^2 is x multiplied by itself twice 
x^1 is x multiplied by 1
x^0 means 'x' is multiplied 0 times, (not even once) to 1 
so, 1* (nothing to multiply) = 1 

yes, its one of the indeterminate forms, others include 0/0, infinity.infinity

solomonzelman · Answer

get it!

solomonzelman · Answer

I always argued w/ my elementary teacher that 0/0 =0 ....

hartnn · Answer

i meant inf/inf

solomonzelman · Answer

still, get it no solush...

solomonzelman · Answer

And anyway, for x^0=1 for any x value beside 0, why is that true?

hartnn · Answer

yup, but no solution sounds weird, there's no equation to solve.
indeterminate form seems accurate

solomonzelman · Answer

Yes

hartnn · Answer

because 1 is the identity of multiplication!

hartnn · Answer

when you take any number 'x' and do not multiply it (0 times), you are only remain with 1

amistre64 · Answer

1*(undefined) is undefined .... not 1

solomonzelman · Answer

you aren't multiplying by itself or a/t it is just to the 0 power.
it is nothing then

amistre64 · Answer

x^0 is a property of the exponential function.

exp(a+b) = exp(a) * exp(b)

exp(n-n) = exp(n) * exp(-n)$$e^n*e^{-n}=\frac{e^n}{e^n}=1$$

solomonzelman · Answer

70%

solomonzelman · Answer

70% get it....

solomonzelman · Answer

Yes I get it....!

solomonzelman · Answer

Thank you! i though there was no logic, but this is just b/c it is 0.... hard to explain and prove that I get it, but I get it.
Thank You again, PRO!!!!

amistre64 · Answer

good luck

solomonzelman · Answer

thank you!