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Lesson 2
The Arithmetic of Powers
Multiplication by addition, and division by subtraction
Well, let’s start with a simple example. Suppose we multiply 31 by 31. The result will be
3 × 3 = 32
will it not? And 32 is a power of 3.
Now, consider multiplying 32 by 31; that is (3 × 3) × 3.
This will result in
3 × 3 × 3 = 33
which is also a power of 3.
If we multiply 33 by 32 we will get (3 × 3 × 3) × (3 × 3), which will be
3 × 3 × 3 × 3 × 3 = 35
won’t it?
In each case the product will be a number that can be reached by using 3 as a factor a sufficient number of times, and therefore will be some power of 3.
Now return to page 41 and choose the right answer.
