Arithmetic of Computers

Well, first, this is a problem in division. Our rule for dividing one power of a number by another power of the same number is

(b^m)/(bⁿ) = b^{(m − n)},

This rule worked fine so long as m was larger than n. For example, we had

(4³)/(4¹) = 4^{(3 − 1)} = 4²

which is correct, as we can find out by checking by ordinary arithmetic:

(4³)/(4¹) = (4 × 4 × 4)/(4) = (64)/(4) = 16

and 16 is equal to 4², isn’t it?

Now, when we tried the case in which m was equal to n, such as 4³ divided by itself, we got

(4³)/(4³) = 4^{(3 − 3)} = 4⁰.

We have not defined 4⁰ yet, which we reached by dividing a power of 4 by itself. But any number divided by itself equals 1, doesn’t it?

(4³)/(4³) = (64)/(64) = 1.

So (4³)/(4³) is equal to 4⁰ by our rule, and is equal to 1 by ordinary arithmetic. And that tells us how to define 4⁰, doesn’t it?

Now return to Page 80 and try again.