Page 1 of 2
Special
Topic
Word Watch
Review Words
power, p. 14
exponent, p. 14
scientific notation, p. 74
reciprocal, p. 222
Negative and Zero Exponents
GOAL Evaluate powers with negative and zero exponents.
In Lesson 1.3, you wrote powers using positive exponents. You can also
use negative integers and zero as exponents.
When you look down the table at the right, notice
that as the exponents for the powers of 2 decrease
by 1, the values of the powers are halved. This
pattern suggests that
1
2
1
2
1
2
1
2
20 2 p 1, 21 1 p 1 ,
1
2
1
2
1
4
1
2
1
4
1
2
1
8
1
2
22 p 2 , and 23 p 3 .
This in turn suggests the following definitions.
Power
Value
3
8
2
4
1
2
2
20
?
1
?
2
?
3
?
2
2
2
2
2
Negative and Zero Exponents
Negative Exponent For any integer n and any nonzero
1
number a, an is the reciprocal of a n. That is, an n .
a
Zero Exponent For any nonzero number a, a0 1.
EXAMPLE
1
Evaluating Powers
Evaluate the power.
a. 53
b. 105
Solution
1
a. 53 3
5
1
125
1
b. 105 5
10
Definition of negative exponent
Evaluate the power.
Definition of negative exponent
1
100,000
Evaluate the power.
0.00001
Write fraction as a decimal.
CONTINUED ON NEXT PAGE
255
Page 2 of 2
Special Topic
Continued
with
Scientific Notation In Lesson 2.5, you
wrote numbers in scientific notation
using positive integers as exponents.
You can also write numbers in scientific
notation using 0 and negative integers as
exponents. To change between scientific
notation and standard form, you can
first write the number as a product with
the power of 10 written as a decimal
in standard form.
Review
Need help with powers
and scientific notation?
See pp. 14 and 74.
Power
1
1
0.1
2
0.01
3
0.001
10
10
10
10
4
10
0.0001
105
0.00001
106
0.000001
7
10
EXAMPLE
2
a. 6 103
EXAMPLE
0.0000001
Writing Numbers in Standard Form
Scientific notation
b. 3.781 10
Standard Form
0
5
3
Product form
Standard form
6 0.001
0.006
3.781 0.00001
0.00003781
Writing Numbers in Scientific Notation
Standard form
a. 0.00059
4 decimal places
b. 0.0000678
5 decimal places
Product form
Scientific notation
5.9 0.0001
5.9 104
Write product.
Exponent is 4.
6.78 0.00001
6.78 105
Write product.
Exponent is 5.
Exercises
Evaluate the power.
1. 62
2. 44
3. 25
4. 106
7. 8.92 103
8. 7.8 106
Write the number in standard form.
5. 2.1 102
6. 6.54 100
9. Art A microscopic sculpture of a bull is about 0.00076 mm wide.
A virus has a width of about 3.6 104 mm. Which is greater, the
width of the sculpture or the width of the virus?
Write the number in scientific notation.
Microscopic bull sculpture
256
CHAPTER 6
10. 0.004567
SPECIAL TOPIC
11. 0.0001
12. 0.00078
13. 0.0000932