why does x^0 always equal 1?

Question

Why does x^0 equal one? My math teacher said something about dividing exponents(subtracting)

Answer 1

Yes, provided x ≠ 0. 0^0 is undefined.

To demonstrate this, since (x^y)/(x^y) = 1, it follows from the rule about subtracting exponents that x^(y-y) = 1, hence x^0 = 1.

Answer 2

You can think about this a lot of ways. First x^1 is of course x itself, and x^-1 is 1/x. Now how do you get from x to 1/x? You divide by x twice, so what if you divided by x just once? You have x/x=1, which is what x^0 is saying, x/x. Now look at it this way, x^0=x^1*x^-1, because any time you multiply two of the same number (in this case x) to different exponenents (1 and -1) you can add the exponenents. So since 0=1+-1, x^0=x^-1*x^1=x/x=1.

Answer 3

Example X^3 divided by X^3 is one as anything divided by itself is one

X^3 divided by X^3 = X^3-3 = X^0

Answer 4

Because x has a 1 in front of it...however it's imaginary...so if it's to the 0 power it's the same as it not being to any power at all...so it's 1 but u drop the x or the variable...sort of like derivatives...
Hope this helps!

Answer 5

(I) is true because f'(x) = (1/3)x^(-2/3) = 1/[3x^(2/3)] > 0. (II) is not true because f'(0) is not defined, let alone not equaling 0. (III) is not true because f'(x) is not strictly continuous on [-1, 1] (x = 0). Therefore, the answer is (a). I hope this helps!

Answer 6

People have already answered this one. I just want you to remember that this happens only if x is different from 0.

Answer 7

Just recall that that is not ture when x = 0. 0^0 is undefined.

Answer 8

Simple, X to the zero power is the same as x to the 1-1 power. x to the minus one power is the reciprocal of x. So miltiply x to its reciprocal i/x and you get one.

Answer 9

I though it was defined that way and there was no derivation or proof required.

Answer 10

i dont think anyone knos y, it just is 1
sry