Exponents are a short-hand notation for writing very large or very. small numbers. The exponent gives the number of times that a number

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1 UNIT 3 EXPONENTS

2 Math 11 Unit 3 Introduction p. 1 of 1 A. Algebraic Skills Unit 3 Exponents Introduction Exponents are a short-hand notation for writing ver large or ver small numbers. The exponent gives the number of times that a number should be multiplied to itself. For example, 3, where the exponent is the raised, 3 indicates that should be multiplied together three times: 3 = = 00. Exponents are used in man disciplines and are especiall useful in science to rewrite extremel large or small numbers. For example, the distance from the earth to the moon is km. Using exponents and scientific notation, this large number can be rewritten as 3.84 km.

3 Math 11 Unit 3 Objectives p. 1 of 1 A. Algebraic Skills Unit 3 Exponents Objectives To evaluate a positive power of a numerical base. To evaluate multiplication and division of positive powers of the same base. To perform the power to a power exponent law. To write numbers in scientific notation and back to standard form. To perform multiplication and division of numbers expressed in scientific notation.

4 Math 11 Unit 3 Outline p. 1 of 1 A. Algebraic Skills Unit 3 Exponents 1. Powers, Bases, and Exponents Exercise 1. Laws of Exponents: Multiplication and Division Exercise 3. Laws of Exponents: Power to a Power Exercise 3 Quiz Scientific Notation Exercise 4. Multiplication and Division of Numbers in Scientific Notation Exercise Unit 3 Review Unit 3 Exam

5 Math 11 Unit 3 Lesson 1 p. 1 of Math 11 Unit 3 Lesson 1 SWBAT evaluate a positive power of a numerical base. 1. Powers, Bases, and Exponents 4 3 exponent base power 4 3 = = 64 exponential (power) expanded numerical form form value Ex. 1. Expand the following powers and find the numerical value. a) 3 = = 8 b) 1 4 = = 1 16 Ex.. Simplif. a) (-) = (-) (-) (-) (-) (-) = -3 b) (-) 6 = (-) (-) (-) (-) (-) (-) = 64

6 Math 11 Unit 3 Lesson 1 p. of Note: If an odd exponent is outside the brackets of a negative number, the answer will be negative. If an even exponent is outside the brackets of a negative number, the answer will be positive. Ex. 3. The following two expressions are ver different. Simplif both. a) (-3) = (-3) (-3) = 9 b) 3 = - (3 3) = -9 Brackets No Brackets Ex. 4. Simplif a) = + ( ) = + 81 = 83 b) - 3 = ( ) ( ) = 4 1 = -11 c) 3 (0 ) + = = = 1 Ex.. Write t t t 3 3 t in exponential form. = t 4 Exercise 1

7 Math 11 Unit 3 Exercise 1 p. 1 of Name: Date: Math 11 Unit 3 Exercise 1 Expand the following powers and find the numerical value (-) 4. (-) 3 3. (-) 7 4. (-1) Rewrite without an exponents (-) 6 1. (-4) (-1) 14. (-) 4 1. (-)

8 Math 11 Unit 3 Exercise 1 p. of Simplif b following the order of operations (BEDMAS) Rewrite using exponents. 8. p p p n n n n n 31. m m m m 3. r r r r w w 4 x x 4 w w x 34. c d k c c d k k k c 3. 3 a a a a

9 Math 11 Unit 3 Lesson p. 1 of Math 11 Unit 3 Lesson SWBAT evaluate multiplication and division of positive powers of the same base.. Laws of Exponents: Multiplication and Division Evaluate: 6 4 = = 6 factors + 4 factors = factors = 6 4 = 6+4 = = 4 Multipling: - to multipl powers with like bases, add the exponents a b = a+ b = = 3 Ex. 1. Evaluate t t. = 3+ t = t Ex.. Evaluate 3. = 3++1 = 6 = 16 Ex. 3. Evaluate ( ) 4 ( ) 1 ( ). 7 = ( ) = -18

10 Math 11 Unit 3 Lesson p. of Dividing: - to divide powers with like bases, subtract the exponents a b or a b = a b or = = Ex. 4. Evaluate b b. = b 1- = b 7 Ex.. Evaluate = 3 = 43 Ex. 6. Evaluate 9. = 1 = The value of an power with an exponent of zero is alwas one. x 0 = = 1 Ex. 7. Evaluate = 4 0 = 1 Exercise

11 Math 11 Unit 3 Exercise p. 1 of Math 11 Unit 3 Exercise Evaluate. 1. r 3 r 4. x 3 x x 4 3. a a h 4 h 3 7. z 7 z x 8 x p p c 16. c k k a 19. a a 17 a 14. c 7 c 11. (-3) (-3)

12 Math 11 Unit 3 Exercise p. of k 7. 9 k 13 c c 9. q 16 q (-6) (-6) 3. (-1) 3 (-1) 4 (-1) (-9) 1 (-9) 3. (-1) (-1)

13 Math 11 Unit 3 Lesson 3 p. 1 of Math 11 Unit 3 Lesson 3 SWBAT perform the power to a power exponent law. 3. Laws of Exponents: Power to a Power To raise a power to a power, multipl the exponents: (x m ) n = x m n (x ) 4 = x 0 Ex. 1. Simplif the expression (m 3 ) 4. = m 3 4 = m 1 Ex.. Simplif the expression (s 1 ). = s 4 Ex. 3. Simplif the expression (b 3 ) 3. = 3 b 9 = 1b 9 Ex. 4. Simplif (a 3 ) (a ) 6. = a 1 a 1 = a 7

14 Math 11 Unit 3 Lesson 3 p. of a 13 Ex.. Simplif ( ) a b b a b a b 1 = 4 6 = a 13-4 b 1-6 = a 9 b 9 Exercise 3

15 Math 11 Unit 3 Exercise 3 p. 1 of Math 11 Unit 3 Exercise 3 Evaluate. 1. ( ) 3. (3 3 ) 3. ( ) 4. (c 4 ) 3. (r 8 ) 4 6. (r 1 ) 7. (k ) 3 8. ( 3 ) 9. (1 ). (3 ) ( 3 ) 4 1. (6 6 ) (x 3 ) 14. (4m ) 3 1. (1r 7 ) 16. (3x ) (6 4 ) 18. (a) (7b ) 3 0. (8f) 4

16 Math 11 Unit 3 Exercise 3 p. of 1. (a ) 3 (a 4 ) 3. (e 6 ) (e 7 ) 3 3. (h 4 ) (h 9 ) 3 4. (b 3 ) 3 (b ). (n ) 3 (n 6 ) r 1 6. ( ) 4 r 3 t 0 7. ( ) 4 t 4 k ( ) 3 k 6 c 9. ( ) c 4 d d 3 8 g 30. ( ) 3 g 1 4 h h 11

17 Math 11 Unit 3 Quiz 1-3 p. 1 of 1 Name: Date: Math 11 Unit 3 Quiz 1-3 Each question is worth 1 mark. 1. Write in expanded form: (7) 4. Write the numerical value: 3 3. Write the numerical value: (-4) 4 4. Simplif: Rewrite using exponents: 4 4 r r t 4 r r t 4 t 6. Simplif: s 6 s 7 7. Simplif: Simplif: (q 4 ) 6 9. Simplif: (x ) r s 1. Simplif: ( 6 3 rs )

18 Math 11 Unit 3 Lesson 4 p. 1 of Math 11 Unit 3 Lesson 4 SWBAT write numbers in scientific notation and back to standard form. 4. Scientific Notation Scientific Notation is used to write ver small or ver large numbers. There are two parts to each number. For example: Largest known star is IRS with diameter km = 1.48 km Mass of electron is g = g The speed of light is km/h. Expressed in scientific notation it is km/h First Part: Place a decimal after the 1 st natural number (1-9). Record the digits that follow, but drop an trailing 0 s. Second Part: A base of to an exponent. The exponent ma be either positive or negative. The exponent is the same number of spaces ou would have to move the decimal from the scientific notation to the standard wa of writing it. * if ou move the decimal to the right, the exponent is positive * if ou move the decimal to the left, the exponent is negative Left Negative Right - Positive Ex. 1. Rewrite each of the following numbers in scientific notation: a) =.3 8 b) = 4. -

19 Math 11 Unit 3 Lesson 4 p. of Ex.. Rewrite the following expressions into standard or decimal form: a) 7.89 = b) = Exercise 4

20 Math 11 Unit 3 Exercise 4 p. 1 of 1 Math 11 Unit 3 Exercise 4 Rewrite using scientific notation , ,000, , , ,7,000, , Rewrite into standard or decimal form

21 Math 11 Unit 3 Lesson p. 1 of Math 11 Unit 3 Lesson SWBAT perform multiplication and division of numbers expressed in scientific notation.. Multiplication and Division of Numbers in Scientific Notation Multipling and Dividing Steps: 1. Group the decimals and the powers of.. Simplif. 3. Express in scientific notation (3 decimal places). Hint: If the number gets larger, the exponent gets smaller. If the number gets smaller, the exponent gets larger. Multipl the following using scientific notation and then express the answer in scientific notation b adjusting the number and the exponent value. Ex. 1. (7 ) (4 3 ) = (7 4) ( 3 ) = 8 8 =.8 9 Ex.. ( 1 ) (4-6 ) = ( 4) ( 1-6 ) = 0 = Ex. 3. (0 - ) (6-7 ) = (0 6) ( - -7 ) = = 3 -

22 Math 11 Unit 3 Lesson p. of Ex. 4. (60 17 ) (3 ) = (60 3) ( 17 ) = 0 1 = Ex.. 13 = (70 ) ( 4 13 ) = 3-9 = Power to a Power: Distribute the exponent to both the number and the exponent. Ex. 6. (3 8 ) 3 = = 7 4 =.7 Ex. 7. (4-11 ) = 4-11 = 16 - = Exercise

23 Math 11 Unit 3 Exercise p. 1 of Math 11 Unit 3 Exercise Simplif. Leave the answer in scientific notation. 1. (4 9 )( 6 ). (3 - )( 1 ) 3. (7 6 )( 3 ) 4. (3-4 )(1 ). ( 3 )( 6 ) 6. (7 - )(3 ) 7. (6-6 )(4 4 ) 8. ( -8 )(8-1 )

24 Math 11 Unit 3 Exercise p. of (4 ) 0. ( 4 ) 6 1. (4 - ) 3. ( -6 ) 3. ( - ) 4 4. ( -4 ) 3. (6 3 )

25 Math 11 Unit 3 Review p. 1 of 4 Name: Date: Math 11 Unit 3 Review 1. Rewrite in exponential form:. Rewrite in exponential form: 3 c d k c c 3 d k k k c 3 Simplif (r r r)(r r r r) 7. ( )( )( ) 8. ( m m m m) ( m m m) r r

26 Math 11 Unit 3 Review p. of p 3 p r r r 0. p 4 p 3 p 1. 8 c. c k n r 4. 3 k n r. (c 4 ) 3

27 Math 11 Unit 3 Review p. 3 of 4 6. (r 3 ) 7. ( ) 4 8. (3a ) ( 3 ) - 3 Rewrite as a standard or decimal number Rewrite using scientific notation

28 Math 11 Unit 3 Review p. 4 of 4 Simplif using scientific notation. 38. (6-4 ) ( ) 39. (4 9 ) ( 6 ) 40. (3. - ) ( 1 ) ( -6 ) 44. (7-4 ) 3 ( 3 4 ) 4. 4

How could you express algebraically, the total amount of money he earned for the three days?

How could you express algebraically, the total amount of money he earned for the three days? UNIT 4 POLYNOMIALS Math 11 Unit 4 Introduction p. 1 of 1 A. Algebraic Skills Unit 4 Polynomials Introduction Problem: Derrek has a part time job changing tires. He gets paid the same amount for each tire