Page 67 - ArithBook5thEd ~ BCC

Apower of a negative number is

• negative if the exponent is odd,
• positive if the exponent is even.

When applying exponents to signed numbers, it is essential to put parentheses around the number,
including its sign. For example, the square of −3 is written

2
(−3) =(−3)(−3) = 9.
Without parentheses, as in
2
−3 ,
2
the exponent applies only to 3, not to −3, and this is not apower of −3. Rather, −3 represents the
2
opposite of 3 ,so
2
−3 = −9.
The behavior of 0 in an exponential expression, in particular, the interpretation of 0 as an exponent,
extends unchanged to signed numbers. (You may wish to review Section 1.4 on powers of whole numbers
in Chapter 1.)

For a nonzero signed number N,
0
• N =1
N
• 0 =0 if N is positive
0
(0 is undefined.)

0
0
4
Example 71. (−3) =1. 0 =0. 0 is undefined.
2.7.1 Exercises

Find the value of each expression.
1. 8 2

2. (−8) 2

3. −8 2

4. −6 3

5. (−6) 3
6. 0 5

3
7. −(−3 )

Page 67