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**Section 1: Using Properties of Exponents**

Chapter 6 Section 1: Using Properties of Exponents

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**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.

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**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

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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

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**Write the following in scientific notation**

325

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VOCABULARY 23 Power - 23 Base – 2 Exponent - 3

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**Recall multiplying 2 powers with the same base:**

2325 (222) (22222) = 28 5453 (5555) (555) = 57

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**PROPERTIES OF EXPONENTS**

Let a and b be real numbers and let m and n be integers. PROPERTY NAME DEFINITION EXAMPLE Product of Powers aman = am+n Quotient of Powers Power of a Power (am)n = amn Power of a Product (ab)m = ambm (continued) 535-1 = 53+(-1) = 52 = 25 (33)2 = 332 = 36 = 729 (23)4 = 2434 = 1296

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**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

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**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

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**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

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**SIMPLIFYING ALGEBRAIC EXPRESSION**

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

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5.1 – Use Properties of Exponents. Example 1: Evaluate Numerical Expressions a. (-4 x 2 5 ) 2 b. (11 5 /11 8 ) -1.

5.1 – Use Properties of Exponents. Example 1: Evaluate Numerical Expressions a. (-4 x 2 5 ) 2 b. (11 5 /11 8 ) -1.

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