9 3 Base. We will apply 1 the properties of exponents. Name:
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1 Learning Objective We will apply the properties of exponents. Name:.2. CFU Activate Prior Knowledge What are we going to do? What does apply mean? Apply means. An exponential expression contains a base raised to an exponent (power). An exponent is the number of times a base is used in multiplication. Write the multiplication problem as an exponential expression = 2. = ial Expression 9 Make Connection Students, you already know that an exponential expression is used to represent repeated multiplication. Now, we will apply properties of exponents. Vocabulary put into action
2 Concept Development Properties 2 of exponents are rules used to simplify exponential expressions. Properties of s Multiplying 2 5 add the exponents. Dividing 4 4 subtract the exponents. Raising to an (5 4 ) multiply the exponents. Simplifying is finished when same bases are combined and there are no negative exponents. 2 5 = = 4 (5 4 ) = 5 4 ial Expression 9 CFU For which of the following exponential expressions can a property of exponents be used? How do you know? A B 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? rules CANNOT be used on the following exponential expressions: Flashcards Rules Vocabulary 2 facts about something
3 Concept Development (continued) Properties of s Raising to a Zero 7 0 Raising to a Negative - - Any base raised to a zero exponent is. Write the expression as a fraction, move the expression to the denominator and change to a positive exponent. Move the expression to the numerator and change to a positive exponent. Simplifying is finished when same bases are combined and there are no negative exponents. 7 0 = - = Concept Demo = = - ial Expression 9 CFU On your whiteboards, give an example of an exponential expression that simplifies to. Which of the following is equal to -2? How do you know? A B C Which of the following is equal to? How do you know? -5 A 5 B 5 C -5
4 Skill Development/Guided Practice Multiplying add the exponents 2 5 = Dividing subtract the exponents 4 = 4 4 Raising to an multiply the exponents ( 2 ) 5 = 2 x 5 Apply the properties of exponents. Identify exponential expressions with the same base. 2 Determine 4 which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. 4 Interpret 5 the exponential expression. simplifies to ial Expression 9 CFU 2 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? Simplifying is finished when same bases are combined and there are no negative exponents Vocabulary find 4 figure out 5 explain
5 Skill Development/Guided Practice 2 Multiplying add the exponents 2 5 = Dividing subtract the exponents 4 = 4 4 Raising to an multiply the exponents ( 2 ) 5 = 2 x 5 Apply the properties of exponents. Identify exponential expressions with the same base. 2 Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. 4 Interpret the exponential expression. simplifies to. ( ) 2 (5 2 ) (2 4 ) ( 2 ) ial Expression 9 CFU 2 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? Simplifying is finished when same bases are combined and there are no negative exponents. (5 ) 2 ( 5 )
6 Skill Development/Guided Practice Raising to a Zero Any base raised to a zero exponent is. 7 0 = Apply the properties of exponents. Identify exponential expressions with the same base. 2 Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. 4 Interpret the exponential expression. simplifies to Raising to a Negative - = = ial Expression 9 CFU 2 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? Simplifying is finished when same bases are combined and there are no negative exponents
7 Relevance Applying properties of exponents will help you simplify exponential expressions faster. 4 4 OR Applying properties of exponents will help you do well on tests. Sample Test Question: 25. Choose Yes or No to indicate whether the expression is equivalent to 7 5. A B C (7 5 ) D CFU 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?
8 Skill Closure Multiplying add the exponents 2 5 = Dividing subtract the exponents Raising to an multiply the exponents Raising to a Zero Any base raised to a zero exponent is. Raising to a Negative 4 - = = 4 ( 2 ) 5 = 2 x = 4 = Apply the properties of exponents. Identify exponential expressions with the same base. 2 Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. 4 Interpret the exponential expression. simplifies to. ial Expression (4 ) Simplifying is finished when same bases are combined and there are no negative exponents. Access Common Core = 28 5 = 2 Summary Closure Caroline simplified the exponential expression to the left incorrectly. Explain the error she made in applying properties of exponents. What did you learn today about applying properties of exponents? (Pair-Share) Use words from the word bank. Word Bank exponents properties raising zero negative
9 Independent Practice Multiplying add the exponents 2 5 = Dividing subtract the exponents Raising to an multiply the exponents Raising to a Zero Any base raised to a zero exponent is. Raising to a Negative 4 - = = 4 ( 2 ) 5 = 2 x = 4 = Apply the properties of exponents. Identify exponential expressions with the same base. 2 Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. 4 Interpret the exponential expression. simplifies to ial Expression 9 Simplifying is finished when same bases are combined and there are no negative exponents. (2 2 ) 4 (2 2 ) 2 5..
10 Independent Practice (continued) Multiplying add the exponents 2 5 = Dividing subtract the exponents Raising to an multiply the exponents Raising to a Zero Any base raised to a zero exponent is. Raising to a Negative 4 - = = 4 ( 2 ) 5 = 2 x = 4 = Apply the properties of exponents. Identify exponential expressions with the same base. 2 Determine which property of exponents to apply. Hint: Look at the operation. Simplify the exponential expression using properties of exponents. 4 Interpret the exponential expression. simplifies to. (7 ) ial Expression 9 Simplifying is finished when same bases are combined and there are no negative exponents
11 Periodic Review (9 4 ) (2 ) (5 2 ) 2 0 ( 2 ) -2 Access Common Core List each property of exponents that will be used to simplify the exponential expression. Then simplify each exponential expression.. (2 ) ( -2 ) 2 2
12 Periodic Review (9 ) Access Common Core. For each problem, describe and correct the error made in applying the properties of exponents. a. 4 5 = 4 5 = 20 b = 7 2 = 7 c = 2 5 = For each problem, describe and correct the error made in applying the properties of exponents. 2a. 2 2 = 2 + = 5 2b = = c. 4 =2 + =2 4. For each problem, describe and correct the error made in applying the properties of exponents. 0 a. = 2 - = b. = 8 - = c. = = For each problem, describe and correct the error made in applying the properties of exponents. 7 4a. = 7 = b. = = c. = 8 2 = 4 8 2
13 Periodic Review. (7 5 ) Access Common Core. Choose Yes or No to indicate whether each expression is equivalent to A B 5-2 C D 5 + (-4) 2. Choose Yes or No to indicate whether each expression is equivalent to. A B C 27 D 8 + (-5). Choose Yes or No to indicate whether each expression is equivalent to (4 2 ) -. A 4 2 B 4-2 C D
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