1. Section 1: Using Properties of Exponents
Chapter 6
Section 1: Using Properties of Exponents

2. Scientific Notation Example: The width of a molecule of water is about
A number is expressed in Scientific Notation if it is in the form c  10n or c X 10n or cEn where 1 |c|  10 and n is an integer.
Example: The width of a molecule of water is about
2.5 X 10-8 meter or
meter.

3. Choose all that apply. Which of the following are in scientific notation?
3.1 x 105
12 x 105
6 x 10-2
0.12 x 10-2
-5 x 103.8

4. In 1997 Denmark had a population of 5,284,000 and a gross domestic product (GDP) of $131, 400, 000, 000. Write the population and GDP in scientific notation.
5,284,000
=5.284 x 106
$131, 400, 000, 000
=$1.314 x 1011

5. Write the following in scientific notation
325

6. VOCABULARY 23
Power - 23
Base – 2
Exponent - 3

7. Recall multiplying 2 powers with the same base:
2325 (222)  (22222) = 28
5453 (5555)  (555) = 57

8. PROPERTIES OF EXPONENTS
 Let a and b be real numbers and let m and n be integers.
PROPERTY NAME DEFINITION EXAMPLE
Product of Powers aman = am+n
Quotient of Powers
Power of a Power (am)n = amn
Power of a Product (ab)m = ambm
(continued)
535-1 = 53+(-1) = 52 = 25
(33)2 = 332 = 36 = 729
(23)4 = 2434 = 1296

9. PROPERTIES OF EXPONENTS
 Let a and b be real numbers and let m and n be integers.
PROPERTY NAME DEFINITION EXAMPLE
Quotient of Powers
Negative Exponent**
Zero Exponent a0 = 1, a  0
Power of a Quotient
(-89)0 = 1

10. EVALUATING NUMERICAL EXPRESSIONS
(23)4
=(8)4
=4096
(-5)-6 (-5)4
=(-5)-6+4
=(-5)-2
(-6*35)3
=(-6*243)3
=(-1458)3
x 109

11. 1 million =1 x 106 85 million =85 x 106 =8.5 x 107
A swarm of locusts may contain as many as 85 million locusts per square kilometer and cover an area of 1200 square kilometers. Write the density of locusts in scientific notation.
1 million =1 x 106
85 million
=85 x 106
=8.5 x 107

12. SIMPLIFYING ALGEBRAIC EXPRESSION
(7b-3)2 b5b
HW: 6.1#18-45x3