Arithmetic of Computers

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Lesson 2

The Arithmetic of Powers

Multiplication by addition, and division by subtraction

Page 61

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Your answer :

(4³)/(4³) = 4^{(3 − 3)} = 4⁰.

You are correct. When we apply the formula

(b^m)/(bⁿ) = b^{(m − n)}

to the case of

(4³)/(4³)

where both m and n are 3, we get

(4³)/(4³) = 4^{(3 − 3)} = 4⁰.

Well, this is something new! When we write this result as a power of 4, we get 4⁰ as our answer.

But does 4⁰ have any meaning? The idea of zero 4’s multiplied together doesn’t see to make much sense, does it?

But now let’s pursue this problem further. We have divided 4³ by 4³ by using the rule for division of powers of numbers and arrived at 4⁰ as the answer. Now let’s try doing this same problem by ordinary arithmetic, without using powers, and see what we get. Which answer is right?

Answer :

(4³)/(4³) = (64)/(64) = 0.