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

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 0.000000025 meter.

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

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

Write the following in scientific notation 325 120 000

VOCABULARY 23 Power - 23 Base – 2 Exponent - 3

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

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

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

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 3099363912 3.099363912 x 109

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

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