Page 27 - ArithBook5thEd ~ BCC

For any nonzero number N,

0
N =1.
0
(0 is undefined.)

This makes sense if you remember the harmless factor of 1 that is understood in every exponential
expression. (You’ll see another justification when you study algebra.)
3
2
0
Although 0 is undefined, expressions such as 0 ,0 , etc., with 0 base and nonzero exponent, make
3
perfect sense (e.g., 0 =0 × 0 × 0= 0).
0
1
5
0
Example 20. 17 =1. 0 =0. 0 =0. 0 is undefined.
1.4.1 Squares and Cubes
Certain powers are so familiar that they have special names. For example, the 2nd power is called the
2
3
square and the 3rd power is called the cube.Thus 5 is read “5 squared,” and 7 is read as “7 cubed.”
The source of these special names is geometric (see Section 1.9). The area of a square, x units on a
2
2
side, is x square units. This means that the square contains x small squares, each one unit on a side.
2
For example, the figure below shows a square 6 units on a side, with area 6 = 36 square units.

=

3
Similarly, the volume of a cube, y units on a side, is y cubic units.This means that the cube
3
contains y little cubes, each one unit on a side. For example, the volume of an ice cube that measures
3
2 cm (centimeters) on a side is 2 = 8 cubic centimeters.
1.4.2 Exercises

1. Rewrite using an exponent: 8 × 8 × 8 × 8

2. Rewrite using an exponent: 4 · 4 · 4 · 4 · 4 · 4

3. Evaluate 2 5

4. Evaluate 9 0
5. Evaluate 0 7

6. Evaluate 5 4

7. Evaluate 10 2

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