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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 where 1 c 10 and n is an integer. Scientific Notation Example: The width of a molecule of water is about 2.5 X 10 -8 meter or 0.000000025 meter.

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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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VOCABULARY Power - 2 3 Base – 2 Exponent - 3 2323

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Recall multiplying 2 powers with the same base: 2 3 2 5 (2 2 2) (2 2 2 2 2) = 2 8 5 4 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) 3 -3099363912 -3.099363912 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 1200 km=1.2 x 10 3 km Density = 8.5 x 10 7 locusts 1.2 x 10 3 km

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SIMPLIFYING ALGEBRAIC EXPRESSION (7b -3 ) 2 b 5 b HW: 6.1#18-45x3, 53

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