why is any number raise to the zero power equals one?

Answer 1

not always. zero to the power zero is not one.

Now for any other no. say x which is not zero,

x^0 = x^(a-a).............a is any constant
=x^a x^-a
=x^a/x^a
=1

Answer 2

In my own words I'd begin to say that your statement is not correct the actual statement is a⁰ = 1, for any a∈ℝ\{0} a⁰ can be written as a^0 = a^(n-n) = (a^n)/(a^n) = 1 except when a = 0, because in that case 0^0 leads to 0/0 and that's why 0⁰ is not 1, in the field of reals Actually what I've written is not a proof, but only the reason why we set a⁰ = 1 To understand better, try to define powers b^n = b times b times b .... times b (repeated for n times) that's what you can find on elementary textbook... but it doesn't work if applied to b^1 b^1 is not the result of a multiplication b^1 = b because that's part of the definition the complete definition of nonnegative integer powers is as follow a⁰ = 1 a¹ = a aⁿ = a· aⁿ⁻¹ this is a recursive definition suppose we want x⁴ x⁴ = x· x³ = x· x· x² = x· x· x· x¹ = x· x· x· x ⁰ ¹ ²

Answer 3

Because the concept of exponent is developed like that. u see:
x=x^1
now we divide both sides of the equation by x and get
x/x = x^1 /x
or, 1= x^1/x^1
or, 1= x^(1-1) [from exponent rule]
or, 1=x^0
now u see solving the prob we divided both sides of the equation by x. But if x=0 then can we do that?? surely not. As far as I think 0^0 is undetermined or some can also say infinity. but i m not sure whether 0^0 is 1 or not. i need to think abt it.
but for all other x except 0, x^0 will be 1.

Answer 4

Lets start with an example.

2 raised to two gives four.
If we divide 2 raised to 2 by two
raised to one, i.e., 4 divided by 2
then we get the quotient as two.
We can also use the formula "a
raised to n divided by a raised
to m = a raised to (n-m)"{In this
case, 2 raised to two divided by
2 raised to one gives 2 raised to
(2-1),i.e. 2.
Here a=2,n=2 & m=1.}
So we can apply this in the following
way:
2 raised to one divided by 2 raised to
one=2/2=1=2 raised to (1-1=0) =2
raised to zero[By using the formula a
raised to n divided by a raised to m=
a raised to (n-m)]

Answer 5

The power 0 of every number except 0 is 1 because-
let x be any number except 0

so, x^0
=x^(m-m),where m is any natural number
=x^m/x^m
=1

it is invalid for x=0 because

0^m/0^m
=0/0 ,which is not defined.

Answer 6

1st of all any number raise to zero is not 1.
number not equal to zero and not equal to infinity(if considered as number) having power zero is 1.
everybody hav explained mathematically,let me explain u by takin 2 school level...
ex. now 2^(2)=2*2=4 ; a^(n)=a.a.a.......a where a not equal to zero and a not equal to infinity and 'n' is finite number less than infinity.
now 'a' not equal 0 , a^(0)=1 coz.. frm defination of raise to power... number is multiplied by itself by 'n'(power) times..
in this case...number is not multiplied by itself even once...also it is not multiplied by 1..but actually if u see...
1xa^(0)=1x('a' not multiplied even once) so we get a^(0)=1
i hope u hav understood..!!theoritically

Answer 7

1 = A^B/A^B = A^(B - B) = A^0

Answer 8

x^0 = x^(1-1) = x^1 / x^1 =1 (where x <> 0)

Answer 9

x^0 = x^(1-1) = x^1 / x^1 =1 (where x <> 0)
by daway it applies fr non zero nos only

Answer 10

for x not = 0
x/x=1
=>x^(1-1)=1
=>x^0=1

i have tried to find out whats the value of 0^0 and does not get 1

Answer 11

correct your question.
only a non-zero number raised to the zero power equals one.
it is an axiom.