Why is it that everything to the ZERO power equals one?
ex:
5^0= 1
234325346^0= 1
Each time you multiply a number by itself you increment the exponent:
A*A=A^2
Each time you divide a number by itself you decrement the exponent:
So...
(A^3)/A = A^2
(A^2)/A = A^1 = A
A/A = 1 = A^0
Hope this helps.
A
it's right
but in fact the best argument
if x is a number
A^x=exp(x*ln(A))
and exp(0)=1
but i don't know if you know exp and log functions lol
If you have a calculator try raising some number to smaller and smaller powers and see what happens.
100^.01 =1.0471
100^.001 =1.00461
100^.0000001 = 1.000000461
Here is another explanation
If you accept the rules of exponents then
x^a/x^a = x^(a-a) = x^0
but x^a/x^a = 1 since any number divided by itself is 1
so x^0 = 1
i don't know what is your level in maths..
so you can write x^a/x^a=1
but,in fact,it's wring because it's not defined for x=0
so your answer is right but in high school it's wrong...
The reason everything to the power of zero equals one is based on the rules of exponents and the concept of the multiplicative identity.
To understand why any number raised to the power of zero equals one, let's consider the basic properties of exponents:
a^m / a^n = a^(m-n)
(a^m)^n = a^(m*n)
Now, let's analyze the pattern when we raise a number to different powers:
1^3 = 1 * 1 * 1 = 1
1^2 = 1 * 1 = 1
1^1 = 1
We can observe that regardless of the exponent we raise 1 to, the result is always 1. This means that 1 is the multiplicative identity for exponentiation, similar to how 0 is the additive identity for addition.
Now, let's examine the same pattern with another number, for example, 5:
5^3 = 5 * 5 * 5 = 125
5^2 = 5 * 5 = 25
5^1 = 5
From the pattern we observed, if we continue this sequence, we would expect 5^0 to be 5 * 0 = 0. However, this is not the case.
The rule that any number raised to the power of zero equals one is established to maintain consistency and allow other rules of exponents to work correctly. It might seem counterintuitive at first, but it has significant applications in mathematics.
Remember, this special case applies when the number being raised to the power of zero is not zero itself.