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You are correct: − 3 − ( − 6) = − 3 + ( + 6) = + 3, not -9.
Well, we had quite a little excursion into addition and subtraction of negative numbers, but we shall need these ideas in studying number systems, so we need to have the subject well in hand.
Now, you recall that we had just defined
b0 = 1
for any b except where b = 0. We reached this definition by noting that our division rule,
(bm)/(bn) = b(m − n)
will give b0 as a result if we apply it to the case of dividing a number by itself. Thus,
(b3)/(b3) = b(3 − 3) = b0
but (b3)/(b3), or any number (except 0) divided by itself equals 1, so we defined b0 = 1.
We used a division process to find a meaning to attach to the exponent 0. Very well, let’s see what other interesting results we can get with this division process. Let’s apply our division rule to the case of (b2)/(b3). What result do we get?
