If any number to the 0 power is 1 then what is 0 to the power!?!?

Question

I asked my professor and was told to find out! >:O

Answer 1

x^0=x^(1-1)=x/x
so, 0^0=0/0
This is an indeterminate quantity, that means its value depends on the situation.
If you know limits then you'll why it is indeterminate by the following example. Consider lim (x->0) x/x and lim (x->0) 2x/x
for the first one the limit is one but for the second one it is 2. But if you put x's value as 0 then both turn into 0/0.

Answer 2

0 to the 0 power is not defined. Here is why.

The concept of power is that A to the Xth power equals A multiplied by itself X times. That's easy for positive integral X: A^1 = A, A^2 = A*A, A^3 = A*A*A, and so on.

The question arose: is it meaningful to talk of A to a power that's fractional? zero? negative? The answer arose out of the fact that if X and Y are positive integers, with X larger than Y, then A^X - A^Y equals A^(X-Y), and A^X * A^Y = A^(X+Y). So A^(1/2) could be defined (and was) as being the positive square root of A (A being a positive number), because A^(1/2) * A^(1/2) would under the rules for adding exponents become A(1/2 + 1/2) = A^1 = A.

That took care of fractional exponents: A^(3/2) could be worked out to be the square root of the cube of A, and so on.

Negative exponents were also easy. A^(-3), for example, is A^3 divided by A^6, equalling A^(3-6), or 1 divided by A^3.

What about zero? As the concept of multiplying a number by itself zero times doesn't mean anything (how would you write it other than with an exponent?) the meaning to give to A^0 had to be worked out from the rules for adding and subtracting exponents. A^0 could be taken to equal A^(1-1), which is A^1 divided by A^1, which is A divided by A, which is 1. So anything to the 0th power equals 1, because it equals the number divided by itself.

That's why the rule doesn't work for a base of 0, because 0^0 is akin to saying 0 divided by 0, and division by 0 isn't allowed. Because you can't get to 0^0 without having a division by 0 embedded somewhere, the number has to remain gloomily undefined.

Answer 3

0 to the power of any number other than 0 is 0

The value 0^0 is quite a debated one and is usually said to be either 0 or 1 (depending on which side you stand on)

Answer 4

it would be 0, since anything times 0 will lawys be itself, powers indicate the amount of time the number is multiplied by itself, so a number to the 0 power will be multipled by not nothing, but the inverse of itself to make it equal to 1. So 0 to the 0 will be equal to 1. However any other power and it will be equal to 0. Weird eh?

Answer 5

a^0, for a=0 non def.
Because a^ -n = 1/ a^n, in this case we'd have 0^0 = 1 / 0^ -0 = 1 / 0^0. if you say 0^0 is 0, the you have:
0 = 1 / 0 !!!
Hope its clr!!!

Answer 6

This would be an indeterminate form. You cannot take 0 and multiply by something and get 1 as is what otherwise happens if we take any non-zero number and raise it to the zeroth power.

Answer 7

Actually, 0 to the 0th power is an indeterminate form. You can't say what it is.

There are seven such indeterminate forms: 0/0, 0*infinity, infinity - infinity, infinity/infinity, 0^0, infinity^0, and 1^infinity. Equations of these forms can take on different values, depending on the context.

Answer 8

0 to the power 0 is stilll 1. Try it on a calculator if you don't believe me!!

Answer 9

0 is the answer

Answer 10

It is certainly not zero but something that is beyond the imagination rather to say that it is imaginery.