Arithmetic of Computers

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Lesson 2

The Arithmetic of Powers

Multiplication by addition, and division by subtraction

Page 43

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Your answer :

(4⁷)/(4²) = 4⁵ (b^m)/(bⁿ) = b^{(m − n)} (7⁴)/(7²) = 49 (3⁹)/(3³) = 3³ ⎫⎬⎭ This group contains a mistake.

You are correct:

(3⁹)/(3³) = 3^{(9 − 3)} = 3^6, not 3³.

Very well, you seem to have a good grasp of the rules for multiplication and division of powers of numbers, stated as follows:

(b^m)(bⁿ) = b^(m + n) (b^m)/(bⁿ) = b^{(m − n)}

Now, let’s go into this matter of exponents a little further. Consider the following division:

(4³)/(4¹) = ?

If you were asked to write the result of this division as a power of 4, what would you write?

Answer :

(4³)/(4¹) = (64)/(4) = 16

Go to Page 52

(4³)/(4¹) = 4^{(3 − 1)} = 4²