Why is any number(except zero) raised to zero is always 1?

250=1 ,  x0=1

Any number except zero) to the zero power always gives one.

Rule of exponents states that

Exponents add when you have the same base. 

So if you have a number, x, and exponents, a and b, then:
x^a multiplied x^b = x^(a+b)
So then if we make one of the exponents negative:x^a multiplied  x^-b = x^(a-b)
And if the exponents are the same magnitude (a = b) x^a  multiplied x^-b = x^a * x^-a = x^(a-a) = x⁰

Now, remember that if you have a negative exponent, it means you have one divided by the number to the exponent:

x^-a = 1/x^a
So, we can also write x^a * x^-a in a different way:
x^a * x^-a = x^a * 1/x^a = x^a/x^a
And a number divided by itself is always 1 so:
x^a * x^-a = x^a* 1/x^a = x^a/x^a = 1:
So now we've shown that:
x^a * x^-a = x^(a-a) = x⁰
and
x^a * x^-a = x^a * 1/x^a:
This means that any number x⁰ = 1.

If you had trouble understanding it all with variables, let's look at it again,but this time as an example with numbers:

If we plug in numbers, (for example let x = 5, a = 2, and b = 4) then:
One rule for exponents is that exponents add when you have the same base.
5² * 5⁴ = 5⁽²⁺⁴⁾ = 5⁶ = 15625
So then, if we make one of the exponents negative:
5² * 5^-4 = 5^(2-4) = 5^-2 = 0:04
And if the exponents are the same magnitude:
5² * 5^-2 = 5^(2-2) = 5⁰

Now, remember that if you have a negative exponent, it means you have one divided by the number to the exponent:
5^-2 = 1/5² = 0:04
So we can also write 5² * 5^-2 in a different way:
5² * 5^-2 = 5² * 1/5² = 5²/5² = 25/25

And a number divided by itself is always 1 so:
5² * 5^-2 = 5² * 1/5² = 5²/5² = 25/25 = 1

So now we've shown that:
5²*5^-2 = 5^(2-2) = 5⁰
and
5² * 5^-2 = 5²/5² = 1
This means that 5⁰ = 1.

This works for any number x that you want to plug in except for x = 0,because 0/0 is indeterminate (it is like dividing zero by zero).

Another explanation

Let's look at what it means to raise a number to a certain power: it means to multiply that number by itself a certain number of times. Three to the second power is three multiplied by itself 2 times, or 3*3=9. Let's look at a few examples:

3⁵ = 3*3*3*3*3 = 243
3⁴ = 3*3*3*3 = 81
3³ = 3*3*3 = 27
3² = 3*3 = 9
3¹ = 3 = 3

But how do you go from 3¹ to 3⁰? If you look at the pattern, you can see that each time we reduce the power by 1 we divide the value by 3. Using this pattern we can not only find the value of 3⁰, we can find the value of 3 raised to a negative power! Here are some examples:

3⁰ = 3/3 = 1
3^-1 = 1/3 = 0.3333... (this decimal repeats forever)
3^(-2) = 1/3/3 = 0.1111...
3^(-3) = 1/3/3/3 = 0.037037...

No matter what number we use when it is raised to the zero power it will always be 1. Suppose instead of 3 we used some number N, where N could even be a decimal. N¹=N, and to reduce the power by 1 we divide by N, soN⁰=N¹/N = N²/2N =1.

Notice that 3^(-1) is the same as 1/(3¹), 3^(-2) is the same as 1/(3⁽²⁾),and so on. This gives us a useful property of exponents, namely that a^(-b) is the same as 1/(a^b).

One more explanation

Heres a quick demonstration of why any number (except zero) raised to the zero power must equal 1. As an example we will let that any number be the number 3.

Note that:
3¹ = 3 = 3
3² = 3*3 = 9
3³ = 3*3*3 = 27
3⁴ = 3*3*3*3 = 81
And so on

Youll notice that 3³=(3⁴)/3, 3²=(3³)/3, 3¹=(3²)/3
In other words, 3^(n-1)=(3ⁿ)/3
So 3⁰=(3¹)/3=3/3=1

This same reasoning will work for any number (not just 3), except the number 0. It wont work for 0 because you cant divide by 0. Lets call any number x:

x^(n-1)=xⁿ/x
So x⁰ = x^(1-1) = x¹/x = x/x = 1

Still another explanation

of the answer is that this is how we've defined powers to be.

Raising something to a power greater than zero means multiplying it by itself a number of times equal to the power. So, for instance,

2¹ = 2
2² = 2 x 2 = 4
2³ = 2 x 2 x 2 = 8
and so on.

Now, you can multiply anything by 1 and it will still be the same thing, and likewise you can divide anything by 1 and it will still be the same. Therefore:

2¹ = 2 x 1 = 2
2² = 2 x 2 x 1 = 4
2³ = 2 x 2 x 2 x 1 = 8

You see I've just multiplied everything by 1.

Now, also note that if you raise something to a negative power, then you take the reciprocal of that something:

2^-1 = 1/2
2^-2 = 1 /(2x2) = 1/4
2^-3 = 1/8

And so on. Again, we can multiply by everything by 1:
2^-1 = 1 x 1/2

Now, what happens when the power is zero?

Well, you're not multiplying by anything, except the 1 you started with. You're not dividing by anything, except the 1 you started with. So, what you're left over with is 1.

Now, here is the slightly more mathematically sophisticated version: when you raise something to a power, what you do is take 1 and multiply it by the base of the power a number of times equal to the power. So, by definition, raising something to the power of zero means you start with 1, and then don't multiply it by anything. So, naturally, 1 is what you're left over with.