Hi Greta,

Mathematicians try to use notation that somehow makes sense. In this case of trying to decide what 0⁰ "should mean", we compare it to other uses of the exponent.

a⁰ = 1 as long as a is positive, so maybe 0⁰ "should be" 1.

0^b = 0 for any ono-zero b, so maybe 0⁰ "should be" 0.

Lets try a^b where a and b are very close to zero, but not zero. This is a calculator exercise.

0.1^0.1 = 0.794328
0.01^0.01 = 0.954993
0.001^0.001 = 0.993116
0.0001^0.0001 = 0.999079

So if a = b and they are both close to zero it looks like 0⁰ "should be" 1.

(1/2)¹ = 1/2
(1/4)^1/2 = 1/2
(1/8)^1/3 = 1/2
(1/16)^1/4 = 1/2
(1/32)^1/5 = 1/2

This time it looks like 0⁰ "should be" 1/2.

It is this confusion that is the problem. There is no value that I would say 0⁰ "should be" this value. The way out of this confusion is just to say that 0⁰ doesn't have a value, that is, it is undefined.

Penny

Go to Math Central