Lesson 1 Properties of Exponents Objective SWBAT write

Lesson 1: Properties of Exponents Objective: SWBAT write powers from a product of repeated factors and evaluate them. Do Now: Problems 1 -4 on the board

Lesson 1: Properties of Exponents Simpler way to write repeated factors is to use exponential notation: 5 x 5 x 5 x 5 base is 5 exponent is 4 Written as a power 54 46 would mean 4 x 4 x 4 x 4

Lesson 1: Properties of Exponents •

Lesson 1: Properties of Exponents A negative number raised to an EVEN power is positive (-3)4 = 81 A negative number raised to an ODD power is negative (-3)3 = -27

Critical Thinking Is (-2)4 the same as -24?

Examples Write in exponential notation and evaluate. 1. 9 x 9 x 9 x 9 2. (-3) x (-3) 3. (1/2) x (1/2) 4. (3. 6) x (3. 6) 5. -n ∙ n ∙ n ∙n Write as repeated factors and evaluate. 1. (-2)5 2. -72 3. (-5)4

Lesson 1: Properties of Exponents Multiplying Powers 32 x 34 = (3 x 3) x (3 x 3 x 3) = 36 (-2)2 x (-2)3 = [(-2) x (-2)] x [(-2) x (-2)] = (-2)5 6 x 63 = 6 x (6 x 6) = 64

Lesson 1: Properties of Exponents Multiplying Powers 45 ∙ 43 = 4__ (-5) ∙ (-5) = (-5)__ General Rule: xa ∙ xb = xa+b **** This rule applies only when the bases are the same ****

Lesson 1: Properties of Exponents Multiplying Powers - Add the exponents 45 ∙ 4 3 = 48 (-5) ∙ (-5) = (-5)2 General Rule: xa ∙ xb = xa+b **** This rule applies only when the bases are the same ****

Examples Write using exponential notation. 1. 53∙ 56 2. (-9) ∙ (-9)3 3. 76 ∙ 70 4. 45 ∙ 4 -2 5. 6 -2 ∙ 6 -5

Critical Thinking What can you conclude when an exponent is 0? 40 ∙ 4 2 =

Critical Thinking What can you conclude when an exponent is 0? 40 ∙ 4 2 = 4 2 Therefore 40 must be ____.

Critical Thinking What can you conclude when an exponent is 0? 40 ∙ 4 2 = 4 2 Therefore 40 must be equal to 1.

Lesson 1: Properties of Exponents Dividing Powers 37 = 3 x 3 x 3 x 3 35 3 x 3 x 3

Lesson 1: Properties of Exponents Dividing Powers 37 = 3 x 3 x 3 x 3 = 3 2 35 3 x 3 x 3

Lesson 1: Properties of Exponents Dividing Powers 79 = 76 (-5)16 = (-5)7

Lesson 1: Properties of Exponents Dividing Powers - Subtract the exponents 79 = 7 3 76 (-5)16 = (-5)9 (-5)7 General Rule: xa = xa-b xb

Lesson 1: Properties of Exponents Zero exponent 34 = 34 -4 = 30 but 3 x 3 x 3 = 1 34 3 x 3 x 3 x 3 Conclusion: 30 = 1 General Rule: x 0 = 1

1. 46 = 4 2. (-7)10 = (-7)4 3. 39 = 27 4. 54 = 54 5. 24 = 27 6. 34 = 3 -8 Examples

Lesson 1: Properties of Exponents A Power to a Power (52)3 means 52 ∙ 52 using the rule for multiplication of powers: 52+2+2 = 56 (84)3 means 84 ∙ 84 = 8__

Lesson 1: Properties of Exponents A Power to a Power – Multiply the exponents (52)3 means 52 ∙ 52 using the rule for multiplication of powers: 52+2+2 = 56 (84)3 means 84 ∙ 84 = 812 Notice the product of the original exponents: General rule: (xm)n = xmn

1. (25)2 2. (w 4)6 3. [(32)3]2 4. (5 x)3 5. (8 x 3)2 Examples

Practice Work Independently: § § § § Guided Practice 1 A Independent Practice 1 A Guided Practice 1 B Independent Practice 1 B Guided Practice 1 C Independent Practice 1 C Handout 1

Closure Why should we use exponential notation? Exit Ticket Homework: Homework 1

Exit Ticket 1. What is the rule for multiplying powers? Example: _____ 2. What is the rule for dividing powers? Example: _____ 3. What is the rule for a power raised to a power? Example: _____

Independent Practice 1 A Answers 1. (-5)4 2. 32 ∙ 5 ∙ q 3 3. m 5 4. 6, 561 5. 1/81 6. 125/343 7. 8, 000, 000 8. 2, 200 mi 9. -311 10. 37 11. 16 12. 10

Independent Practice 1 B Answers 1. (-6)7 2. -24 a 10 3. -35 a 5 b 5 c 5 4. 82 5. 2 t 3 6. x 2 y 5 8. 4 ∙ 5 ∙ 6 or 120 9. 65 or 7, 776 7. 33 x 2 or 27 x 2 10. (-2)2 ∙ (-3)3 ∙ (-5) or 540 11. 1014 instructions 12. 34 or 81 times

Independent Practice 1 C Answers 1. 46 2. 59 3. d 42 4. h 36 5. 38 6. 58 7. 54 j 24 or 625 j 24 8. 113 c 12 or 1331 c 12 9. 63 a 6 b 18 or 216 a 6 b 18

Independent Practice 1 C Answers 10. 26 m 30 n 66 or 64 m 30 n 66 11. (-3)5 w 15 z 40 or -243 w 15 z 40 12. (-5)4 r 16 s 48 or 625 r 16 s 48 13. (3 c 6 d 2)3 or 27 c 18 d 6 14. (3 w 4)3 or 27 w 12

Independent Practice 1 C Answers 15. 729 x 12 y 18 16. 9 a 12 b 18 25 17. -2048 v 29