290 CHAPTER 5 Number Theory and the Real Number System Section 5.6 Rules of Exponents Product rule for exponents: ⋅ = + a a a m n m n Quotient rule for exponents: = ≠ − a a a a , 0 m n m n Zero exponent rule: a a 1, 0 0 = ≠ Negative exponent rule: a a a 1 , 0 m m = ≠ − Power rule: a a ( )m n m n = ⋅ Scientific Notation Scientific notation is used to write very small or very large numbers. Each number in scientific notation is written as a number greater than or equal to 1 and less than 10 multiplied by an integer power of 10. Examples 1–5, pages 265–267 Discussion pages 268–270, Examples 6–12, pages 268–271 Section 5.7 Arithmetic Sequence General or nth term: = + − a a n d ( 1) n 1 Sum of the first n terms: s n a a ( ) 2 n n 1 = + Geometric Sequence General or nth term: = − a a r n n 1 1 Sum of the first n terms: s a r r r (1 ) 1 , 1 n n 1 = − − ≠ Discussion page 275, Examples 1–5, pages 275–277 Discussion pages 277–279, Examples 6–10, pages 278–279 Section 5.8 Fibonacci Sequence … 1, 1, 2, 3, 5, 8, 13, 21, Golden Number + ≈ 5 1 2 1.618 Golden Proportion + = a b a a b Discussion pages 282–286, Example 1, page 284 Discussion pages 284–286 Discussion pages 284–286 5.1 In Exercises 1 and 2, determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, and 10. 1. 158,340 2, 3, 4, 5, 6, 10 2. 400,644 2, 3, 4, 6, 9 In Exercises 3 and 4, determine the prime factorization of the number. 3. 540 ⋅ ⋅ 2 3 5 2 3 4. 1452 ⋅ ⋅ 2 3 11 2 2 In Exercises 5 and 6, determine the GCD and LCM of the numbers. 5. 30, 105 15; 210 6. 63, 108 9; 756 Review Exercises CHAPTER 5 7. Airport Activity O’Hare International Airport in Chicago has a flight leaving for New York City every 45 minutes and a flight leaving for Washington, DC, every 60 minutes. If a flight to New York City and a flight to Washington, DC, leave at the same time, how many minutes will it be before a flight to New York City and a flight to Washington, DC, again leave at the same time? 180 minutes 5.2 In Exercises 8–13, use a number line to evaluate the expression. 8. + − 4 ( 5) −1 9. − + 2 5 3 10. 2 ( 4) − + − −6 11. − 4 8 4−
RkJQdWJsaXNoZXIy NjM5ODQ=