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Section 1: Using Properties of Exponents Chapter 6

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

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Choose all that apply. Which of the following are in scientific notation? A)3.1 x 10 5 B)12 x 10 5 C)6 x D)0.12 x E)-5 x

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5,284,000 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. $131, 400, 000, 000 =5.284 x 10 6 =$1.314 x 10 11

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Write the following in scientific notation

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VOCABULARY Power Base – 2 Exponent

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Recall multiplying 2 powers with the same base: 2 3 2 5 (2 2 2) (2 2 2 2 2) = 5 3 (5 5 5 5) (5 5 5) = 5 7

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Let a and b be real numbers and let m and n be integers. PROPERTY NAME DEFINITION EXAMPLE Product of Powers a m a n = a m+n Quotient of Powers Power of a Power (a m ) n = a mn Power of a Product (ab) m = a m b m (continued) PROPERTIES OF EXPONENTS 5 3 5 -1 = 5 3+(-1) = 5 2 = 25 (3 3 ) 2 = 3 3 2 = 3 6 = 729 (2 3) 4 = 2 4 3 4 = 1296

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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 a 0 = 1, a 0 Power of a Quotient PROPERTIES OF EXPONENTS (-89) 0 = 1

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EVALUATING NUMERICAL EXPRESSIONS (2 3 ) 4 (-5) -6 (-5) 4 (-6*3 5 ) 3 =(8) 4 =4096 =(-5) -6+4 =(-5) -2 =(-6*243) 3 =(-1458) x 10 9

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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. 85 million 1 million =1 x 10 6 =85 x 10 6 =8.5 x 10 7

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SIMPLIFYING ALGEBRAIC EXPRESSION (7b -3 ) 2 b 5 b HW: 6.1#18-45x3

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