Arithmetic of Computers

Lesson 2

The Arithmetic of Powers

Multiplication by addition, and division by subtraction

Page 60

We can write out 2⁷ and 2⁴ in full to show again why the number of times the base (2 in this case) occurs as a factor in the quotient is the difference between the number of times it occurs as a factor in the dividend (2⁷) and the number of times in the divisor (2⁴):

(128)/(16) = (2⁷)/(2⁴) = (2 × 2 × 2 × 2 × 2 × 2 × 2)/(2 × 2 × 2 × 2) = 2 × 2 × 2 = 8.

The cancellation of 2’s in the dividend and divisor leaves three 2’s to be used as factors in forming the quotient.

Here are four sets of operations involving exponents and powers of numbers. Pick out the group containing a mistake.

Answer :

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

Go to Page 43

(b¹⁶)/(bⁿ) = b^{(16 − n)} (5³)/(5¹) = 25 (10⁴)/(10²) = 100 (b²)/(b) = b¹ ⎫⎬⎭ This group contains a mistake.

Go to Page 46

(4⁵)/(4²) = 64 (6^m)/(6³) = 6^{(m − 3)} (4³)/(4²) = 4 (12²)/(12) = 12 ⎫⎬⎭ This group contains a mistake.

Go to Page 67

((8²)(8⁴))/(8³) = (8⁶)/(8³) = 8³ (b¹⁰)/(b⁷) = b³ (3³)/(3¹) = 9 (6³)/(6) = 36 ⎫⎬⎭ This group contains a mistake.

Go to Page 88

Answer to Self-Test Question 15, Lesson 2 :

(2⁵)/(2³) = 2² = 4.