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Lesson 2
The Arithmetic of Powers
Multiplication by addition, and division by subtraction
Well, you agree, don’t you, that 72 = 7 × 7, which means that 7 is to be used as a factor twice? And you agree that 73 = 7 × 7 × 7, which means that 7 is to be used as a factor 3 times? Let’s try writing it out to see if it will help make the whole situation clear:
72
= (7 × 7)
73
= (7 × 7 × 7)(7 × 7) × (7 × 7 × 7)
= (7 × 7 × 7 × 7 × 7)
= 7 used as a factor five times
= 75
We could reach the same answer by adding the exponents in the product, thus:
