1. Chapter 4 Radicals/Exponents

2. §4.2 Irrational Numbers

3. Real Numbers: All Numbers  Positive & Negative Numbers with a decimal representation that neither terminates nor repeats  Negative and Positive Numbers  Cannot be written as a fraction. Ex: π, √ 2, √ -50 Numbers with a decimal representation that terminates or repeats  Negative and Positive Numbers  Can be written as a fraction. Ex: 5.3, -16.381, ¾, √, 0.8 2 Irrational Numbers: Rational Numbers: Negative and Positive whole numbers  No Decimals Ex: -4, -3, -2, -1, 0, 1, 2, 3, 4 Integers: 3 9 64

4. Only positive numbers.  No decimals or fractions  Includes 0 Ex: 0, 1, 2, 3, 4, …. Only positive numbers  No decimals or fractions  Does not include 0. Ex: 1, 2, 3, 4, 5, 6, …. Whole Numbers: Natural Numbers:

5. Label the following as Rational or Irrational: 1.2.3. 4.5.6. Irrational = 4 Rational Irrational = 1.2 Rational = ⅔ Rational Irrational

6. Types of NumbersRealIrrationalRationalIntegerWholeNatural -5 0 0.12112111… -0.75 Put a check mark in the box that describes the number given. (Some numbers may require more than one check.)

7. What type of number is ? INatural IIInteger III Rational IVIrrational = -6 Natural #s are Positive Irrational #s are non-terminating/ non-repeating decimals D) II & III

8. §4.3 Mixed and Entire Radicals

9. Simplify each radical a) 80 2 40 220 210 25 2

10. Simplify each radical b) c) 2 72 236 2 18 2 9 2 81 327 3 9 3 3 3 3

11. Example 2: Write each radical in simplest form, if possible. a) b) c) 2 20 210 2 5 2 13 Can not simplify 2 16 2 8 2 4 2 2

12. §4.4 Fractional Exponents and Radicals

13. Review of Exponent Laws Law #1 – When multiplying variables we ______the exponents 1) 2) 3) 4) ADD Why do we add the exponents? (x·x·x·x)(x) =x·x·x·x·x = x 5 Must have the same Base

14. Review of Exponent Laws Law #2 – When dividing variables we __________ the exponents. 1) 2) 3) 4) SUBTRACT Why do we subtract the exponents? x·x·x·x·x·x x·x = x·x·x·x= x 4 Must have the same Base

15. Review of Exponent Laws Law #3 & #4 1) 2) 3) 4) 5) Why? (x3)2(x3)2 = (x·x·x)(x·x·x) = x 6 (xy) 3 = (xy)(xy)(xy) = x 3 y 3 = x·y·x·y·x·y = x·x·x·y·y·y

16. Review of Exponent Laws Law #5 1) 2) 3) 4) Why? xyxy ( ) 3 = xyxy xyxy xyxy = x∙x∙x y∙y∙y = x3y3x3y3

17. Review of Exponent Laws Radical FormPower Form Law #6 Example 1: Evaluate each power without using a calculator a)b) c)d)

18. Example 2: Write the following in radical form. a)b) c)d)

19. Example 3: Write the following in power form. a)b) c)d)

20. Example 4: Evaluate a)b) c)d) Calculator: 1.8 ^ (7 ÷ 5)

21. Biologists use the formula to estimate the brain mass, b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass of each animal a) a husky with body mass 27 kg b) a polar bear with a body mass of 200 Kg Calculator: 0.01 x (200 ^ (2 ÷ 3)) a b / c or

22. §4.5 Negative Exponents and Reciprocals

23. Review of Exponent Laws Law #7 – Anything (number or variable) with a power of zero will equal 1. 1) 2) 3)

24. Review of Exponent Laws Law #8 If there is a negative power flip it to opposite side of the fraction. (Reciprocal) 1)2) 3)4)

25. Review of Exponent Laws Law #8 If there is a negative power flip it to opposite side of fraction. (Reciprocal) 5) 6)

26. Example 1: Evaluate each power a)b) c) Use a Calculator 0.3 ^ -4 =

27. Example 2: Evaluate each power without using a calculator a)b) c)

28. Palaeontologists use measurements from fossilized dinosaur tracks and the formula to estimate the speed at which the dinosaur travelled. In the formula, v is the speed in metres per second, s is the distance between successive footprints of the same foot, and f is the foot length in metres. Use the measurements in the diagram to estimate the speed of the dinosaur. Calculator: 0.155 x (1 ^ (5 ÷ 3)) x (0.25 ^ (-7 ÷ 6)) a b / c or

29. §4.6 Applying the Exponent Laws

30. Example 1: Simplify by writing as a single power. a) b) Single Power

31. Example 1: Simplify by writing as a single power. c) d)

32. Example 2: Simplify a) b) Can’t have negative powers in answer

33. Example 2: Simplify c) d)

34. Simplify each of the following (No Calculators!) e) f) Can’t have negative powers in answer

35. A sphere has a volume of 425 cubic metres. What is the radius of the sphere to the nearest tenth of a metre? 3· ·3 1275 = 4πr 3 4π4π 4π4π 1275 = r 3 4π √ 3 √ 3 Calculator: 3 √((1275 ÷ (4xπ))= 4.7m = r