1. 2. 3  3  3  3  What are we going to do? What does apply mean? Apply means __________. CFU Students, you already know that an exponential expression is used to represent repeated multiplication. Now, we will apply properties of exponents. Make Connection 1 put into action Vocabulary We will apply 1 the properties of exponents. Learning Objective Activate Prior Knowledge An exponential expression contains a base raised to an exponent (power). An exponent is the number of times a base is used in multiplication. Exponent Base Exponential Expression 9393 3434 4545 Write the multiplication problem as an exponential expression. 1. 4  4  4  4  4  Name:____________________ 11.21.13

2. 2 facts about something Vocabulary Concept Development Properties 2 of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. 3 2  3 5 Keep the base, add the exponents. 3 2 × 3 5 = 3 2 + 5 Dividing 4 6 4 3 Keep the base, subtract the exponents. = 4 6  3 Raising to an Exponent (5 4 ) 3 Keep the base, multiply the exponents. (5 4 ) 3 = 5 4 × 3 Properties of Exponents 46434643 Go to Skill Dev 1Go to Skill Dev 2 Exponent rules CANNOT be used on the following exponential expressions: 5 2 × 4 3 34433443 Flashcards Exponent Rules For which of the following exponential expressions can a property of exponents be used? How do you know? A 3 4 × 2 4 B 4 3 × 4 2 How do you know a property of exponents CANNOT be used on the other exponential expression? What is the difference between the property of exponents for Multiplying and Dividing ? CFU 1 Which of following shows the property of exponents correctly used for the expression (4 3 ) 2 ? A 4 3 + 2 B 4 3 × 2 C 4 3 − 2 CFU 2 Exponent Base Exponential Expression 9393 Multiplying Simplifying is finished when same bases are combined and there are no negative exponents. Concept Demo

3. On your whiteboards, give an example of an exponential expression that simplifies to 1. Which of the following is equal to 3 -2 ? How do you know? A B C Which of the following is equal to ? How do you know? A B C CFU 3 1 6 -5 1 3232 1 3 -2 1 1 6565 6 -5 1 6565 1 Raising to a Zero Exponent 7 0 Any base raised to a zero exponent is 1. 7 0 = 1 Raising to a Negative Exponent 6 -3 Write the expression as a fraction, move the expression to the denominator and change to a positive exponent. 1 6 -3 Move the expression to the numerator and change to a positive exponent. Go to Skill Dev 3 Exponent Base Exponential Expression 9393 Concept Development (continued) 1 6363 6 -3 = 1 = 6363 1 6363 = Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Properties of Exponents Simplifying is finished when same bases are combined and there are no negative exponents. Concept Demo

4. 3 2  3 5 = 3  3  3  3  3  3  3 ()() 1234567 2+5= 7 3 2  3 5 = 3 2 + 5 = 3 7 Explain to your partner why the property for Multiplying Exponents can be used. CFU 46434643 4  4  4  4  4  4 4  4  4 = 123 46434643 = 4 6  3 = 4 3 Explain to your partner why the property for Dividing Exponents can be used. CFU (5 4 ) 3 = 5 × 5 × 5× 5 × 5 × 5 × 5× 5 ()()() 123 1 2345 67 89 101112 (5 4 ) 3 = 5 4 × 3 = 5 12 Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. 73737373 7070 = 7 3  3 == 1 63636363 × 6 -3 = 6 -3 × 6 3 6 3 = 60636063 = 163163 Concept Development (Clarification and CFU) Explain to your partner why the property for Raising to an Exponent can be used. CFU Explain to your partner why the property for Raising to a Zero Exponent can be used. CFU Explain to your partner why the property for Raising to a Negative Exponent can be used. CFU Properties of Exponents Click each button once to play animation and again to clear.

5. Identify 3 exponential expressions with the same base. Determine 4 which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. Interpret 5 the exponential expression. “ ____ simplifies to ____.” Apply the properties of exponents. 1 2 3 4 Back to Concept Dev 3 find 4 figure out 5 explain Vocabulary How did I/you identify exponential expressions with the same base? How did I/you determine which property of exponents to apply? How did I/you simplify the exponential expression? CFU 1 2 3 Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Multiplying Keep the base, add the exponents 3 2  3 5 = 3 2 + 5 Dividing Keep the base, subtract the exponents = 4 6  3 Raising to an Exponent Keep the base, multiply the exponents (3 2 ) 5 = 3 2 x 5 46434643 Skill Development/Guided Practice 1 Exponent Base Exponential Expression 9393 1.2. 3.4. 5.6. 7.8. 2 2 × 2 4 = 2 2 + 4 = 2 6 3 2 × 3 3 = 3 2 + 3 = 3 5 = 64 “2 2 × 2 4 simplifies to 64” = 243 “3 2 × 3 3 simplifies to 243” 67646764 = 6 7  4 = 6 3 = 216 “ simplifies to 216” 67646764 56525652 = 5 6  2 = 5 4 = 625 “ simplifies to 625” 56525652 4 3 × 4 2 3 5 4 3 + 2 3 5 = 45354535 = 1024 243 = “ simplifies to ” 4 3 × 4 2 3 5 1024 243 2 2 × 2 3 5 3 2 2 + 3 5 3 = 25532553 = 32 125 = “ simplifies to ” 2 2 × 2 3 5 3 32 125 3 2 × 4 74 = 3 2 × 4 7  4 = 3 2 × 4 3 = 9 × 64= 576 “ simplifies to 576” 3 2 × 4 74 2 2 × 5 8 5 7 = 2 2 × 5 8  7 = 2 2 × 5 1 = 4 × 5= 20 “ simplifies to 20” 2 2 × 5 8 5 7 Simplifying is finished when same bases are combined and there are no negative exponents.

6. Identify exponential expressions with the same base. Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. Interpret the exponential expression. “ ____ simplifies to ____.” Apply the properties of exponents. 1 2 3 4 How did I/you identify exponential expressions with the same base? How did I/you determine which property of exponents to apply? How did I/you simplify the exponential expression? CFU 1 2 3 Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Multiplying Keep the base, add the exponents 3 2  3 5 = 3 2 + 5 Dividing Keep the base, subtract the exponents = 4 6  3 Raising to an Exponent Keep the base, multiply the exponents (3 2 ) 5 = 3 2 x 5 Skill Development/Guided Practice 2 Exponent Base Exponential Expression 9393 1.2. 3.4. 5.6. = 3 3 × 2 = 3 6 (3 3 ) 2 = 729 “(3 3 ) 2 simplifies to 729” = 5 2 × 2 = 5 4 (5 2 ) 2 = 625 “(5 2 ) 2 simplifies to 625” (2 4 ) 2 × 2 2 = 2 4 × 2 × 2 2 = 2 8 × 2 2 = 2 8 + 2 = 2 10 = 1024 “(2 4 ) 2 × 2 2 simplifies to 1024” (3 2 ) 2 × 3 3 = 3 2 × 2 × 3 3 = 3 4 × 3 3 = 3 4 + 3 = 3 7 = 2187 “(3 2 ) 2 × 3 3 simplifies to 2187” (5 3 ) 2 5 3 5 3 × 2 5 3 = 56535653 = = 5 6  3 = 5 3 = 125 “ simplifies to 125” (5 3 ) 2 5 3 (6 5 ) 2 6 7 6 5 × 2 6 7 = 6 10 6 7 = = 6 10  7 = 6 3 = 216 “ simplifies to 216” (6 5 ) 2 6 7 Back to Concept Dev 46434643 Simplifying is finished when same bases are combined and there are no negative exponents.

7. Identify exponential expressions with the same base. Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. Interpret the exponential expression. “ ____ simplifies to ____.” Apply the properties of exponents. 1 2 3 4 How did I/you identify exponential expressions with the same base? How did I/you determine which property of exponents to apply? How did I/you simplify the exponential expression? CFU 1 2 3 Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Skill Development/Guided Practice 3 Exponent Base Exponential Expression 9393 1.2. 3.4. 5.6. Raising to a Zero Exponent Any base raised to a zero exponent is 1. 7 0 = 1 Raising to a Negative Exponent 1 6363 6 -3 = 6363 = 1 6363 = 19090 “9 0 simplifies to 1” = 16060 “6 0 simplifies to 1” 5 -3 1 = 153153 = 125 = “ 5 -3 simplifies to ” 1 125 3 -2 1 = 132132 = 1919 = “ 3 -2 simplifies to ” 1919 1 7 -2 721721 = = 49 “ simplifies to 49” 1 7 -2 1 4 -3 431431 = = 64 “ simplifies to 64” 1 4 -3 Simplifying is finished when same bases are combined and there are no negative exponents.

8. Applying properties of exponents will help you simplify exponential expressions faster. Applying properties of exponents will help you do well on tests. 1 Does anyone else have another reason why it is relevant to apply properties of exponents? (Pair-Share) Why is it relevant to apply properties of exponents? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU 2 Relevance ×44×4×4×4× 4 ×44×4 OR 4343 4646 4343 4 6  3 4343 4646 4343 Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Sample Test Question: 25. Choose Yes or No to indicate whether the expression is equivalent to 7 15. O Yes O No A 7 10 × 7 5 B 7 5 × 7 3 C (7 5 ) 4 × 7 -4 D 7 15 × 7 0

9. Skill Closure Access Common Core Summary Closure Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Identify exponential expressions with the same base. Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. Interpret the exponential expression. “ ____ simplifies to ____.” Apply the properties of exponents. 1 2 3 4 Multiplying Keep the base, add the exponents 3 2  3 5 = 3 2 + 5 Dividing Keep the base, subtract the exponents = 4 6  3 Raising to an Exponent Keep the base, multiply the exponents (3 2 ) 5 = 3 2 x 5 Raising to a Zero Exponent Any base raised to a zero exponent is 1. 7 0 = 1 Raising to a Negative Exponent 46434643 1 6363 6 -3 = 6363 = 1 6363 Exponent Base Exponential Expression 9393 What did you learn today about applying properties of exponents? (Pair-Share) Use words from the word bank. Caroline simplified the exponential expression to the left incorrectly. Explain the error she made in applying properties of exponents. 48254825 = 2 8  5 = 2 3 1.2.3. 4 3 × 4 2 = 4 3 + 2 = 4 5 = 1024 “4 3 × 4 2 simplifies to 1024” (4 3 ) 2 = 4 3 × 2 = 4 6 = 4096 “(4 3 ) 2 simplifies to 4096” 4 -3 1 = 143143 = 64 = “4 -3 simplifies to ” 1 64 Simplifying is finished when same bases are combined and there are no negative exponents. Word Bank exponents properties raising zero negative

10. Independent Practice Identify exponential expressions with the same base. Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. Interpret the exponential expression. “ ____ simplifies to ____.” Apply the properties of exponents. 1 2 3 4 Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Multiplying Keep the base, add the exponents 3 2  3 5 = 3 2 + 5 Dividing Keep the base, subtract the exponents = 4 6  3 Raising to an Exponent Keep the base, multiply the exponents (3 2 ) 5 = 3 2 x 5 Raising to a Zero Exponent Any base raised to a zero exponent is 1. 7 0 = 1 Raising to a Negative Exponent 46434643 1 6363 6 -3 = 6363 = 1 6363 Exponent Base Exponential Expression 9393 1.2. 3.4. 5.6. 5 2 × 5 2 = 5 2 + 2 = 5 4 = 625 “5 2 × 5 2 simplifies to 625” 35323532 = 3 5  2 = 3 3 = 27 “ simplifies to 27” 35323532 2 2 × 2 2 5 2 2 2 + 2 5 2 = 24522452 = 16 25 = “ simplifies to ” 2 2 × 2 2 5 2 16 25 4 2 × 6 9 6 7 = 4 2 × 6 9  7 = 4 2 × 6 2 = 16 × 36= 576 “ simplifies to 576” 4 2 × 6 9 6 7 = 2 2 × 4 = 2 8 (2 2 ) 4 = 256 “(2 2 ) 4 simplifies to 256” (2 2 ) 3 × 2 = 2 2 × 3 × 2 1 = 2 6 × 2 1 = 2 6 + 1 = 2 7 = 128 “(2 2 ) 3 × 2 simplifies to 128” Simplifying is finished when same bases are combined and there are no negative exponents.

11. Independent Practice (continued) Identify exponential expressions with the same base. Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. Interpret the exponential expression. “ ____ simplifies to ____.” Apply the properties of exponents. 1 2 3 4 Properties of exponents are rules used to simplify exponential expressions. Properties of exponents can only be used when two exponential expressions have the same base. Multiplying Keep the base, add the exponents 3 2  3 5 = 3 2 + 5 Dividing Keep the base, subtract the exponents = 4 6  3 Raising to an Exponent Keep the base, multiply the exponents (3 2 ) 5 = 3 2 x 5 Raising to a Zero Exponent Any base raised to a zero exponent is 1. 7 0 = 1 Raising to a Negative Exponent 46434643 1 6363 6 -3 = 6363 = 1 6363 Exponent Base Exponential Expression 9393 Simplifying is finished when same bases are combined and there are no negative exponents. 7.8. 9.10. (7 3 ) 3 7 6 7 3 × 3 7 6 = 79767976 = = 7 9  6 = 7 3 = 343 “ simplifies to 343” (7 3 ) 3 7 6 = 111 0 “11 0 simplifies to 1” 8 -2 1 = 182182 = 64 = “ 8 -2 simplifies to ” 1 64 1 9 -3 931931 = = 729 “ simplifies to 729” 1 9 -3

12. Periodic Review 1 Access Common Core 1.2. 3.4. 5.6. (9 4 ) 3 9 12 = 1 6 5 × 6 4 6 11 1 36 = (2 3 ) 2 × 5 2 = 1600 45464546 1414 = (5 2 ) 2 × 6 0 = 625 (3 2 ) -2 1 81 = List each property of exponents that will be used to simplify the exponential expression. Then simplify each exponential expression. 1. (2 3 ) -2 × 5 -4 × 5 7 2. 3. (3 -2 ) 2 × 3 6 × 2 3 2 5 × 6 -2 2 4 × 9 0

13. Periodic Review 2 Access Common Core 1.2. 3.4. 1 8 -3 = 512 53705370 (9 3 ) 0 × 2 3 = 8 4 2 4 -1 = 125 = 64 1. For each problem, describe and correct the error made in applying the properties of exponents. 1a. 6 4 × 6 5 = 6 4 × 5 = 6 20 1b. 7 3 × 7 2 = 7 3 × 2 = 7 6 1c. 2 5 × 2 3 = 2 5 × 3 = 2 15 2a. 3 2 × 2 3 = 6 2 + 3 = 6 5 2b. 5 2 × 5 2 = 25 2 + 2 = 25 4 2c. 4 3 × 3 1 = 12 3 + 1 = 12 4 2. For each problem, describe and correct the error made in applying the properties of exponents. 3. For each problem, describe and correct the error made in applying the properties of exponents. 4. For each problem, describe and correct the error made in applying the properties of exponents. 3a. = 2 6 - 3 = 2 3 10 6 5 3 3b. = 3 8 - 6 = 3 2 98369836 3c. = 4 9 - 5 = 4 4 12 9 3 5 4a. = 7 6 ÷ 3 = 7 2 76737673 4b. = 5 10 ÷ 2 = 5 5 5 10 5 2 4c. = 3 8 ÷ 2 = 3 4 38323832

14. Periodic Review 3 Access Common Core 1.2. (7 5 ) 3 7 17 10 5 × 10 6 10 7 1 49 = = 10,000 1. Choose Yes or No to indicate whether each expression is equivalent to 5 3 × 5 -4. O Yes O No A B 5 -12 C D 5 3 + (-4) 53545354 1515 2. Choose Yes or No to indicate whether each expression is equivalent to. O Yes O No A 3 8 × 3 -5 B 3 3 C D 3 8 + (-5) 1 27 38353835 3. Choose Yes or No to indicate whether each expression is equivalent to (4 2 ) -1. O Yes O No A B 4 -2 C 4 4 × 4 -6 D 16 142142