Question

When a number has an exponent of zero, why does it equal 1? Shouldn't it be 0?

Answer 1

anything to the power of 0 = 1

Answer 2

anything but 0.

Answer 3

\[0^0\neq0\]

Answer 4

if all fails use the calculator

Answer 5

I know it equals 1, but I want to know why.

Answer 6

no because the rule is 0 exponents always equal 1

Answer 7

why do you want to know why

Answer 8

math teacher told our class to find out

Answer 9

I guess you can prove it by stating this :
x^y = x^a * x^b (provided that y = a+b)
If b = 0, x^b needs to =1, else you'd have
x^a * 0 = 0 =/= x^y

Answer 10

so by having x^0 = 1, x^a * 1 = x^a = x^(a+0) = x^y. Makes sense?

Answer 11

can u plug in numbers to that as an example please?

Answer 12

consider a^1 ÷ a^1 = a / a = 1
but as per laws of indices, a / a = a^(1 – 1) = a^0 = 1
consider a^2 ÷ a^2 = a × a / a × a = 1
but as per laws of indices, a^2 / a^2 = a^(2 – 2) = a^0 = 1
or 5^3 ÷ 5^3 = 125 / 125 = 1
and 5^3 ÷ 5^3 = 5^(3 – 3) = 5^0 = 1
this shows that any number with exponent 0 is equal to 1

Answer 13

ah, yes, I much prefer intedralsabiti's proof than mine, a lot simpler

Answer 14

his proof also proves that 0^0 doesn't work because you'd need to divide 0 by 0.
0^2/0^2 is impossible, so 0^(2-2) also is, and finally, 0^0 is impossible as well.

Answer 15

i dont deserve that medal.take it back. It is copy-paste

Answer 16

bah, then it's a medal for google-searching skills ;-) whatever works really

Answer 17

thx :D