Lesson 1 NYS COMMON CORE MATHEMATICS CURRICULUM 8β’1 Lesson 1: Exponential Notation Classwork π π ππ means π × π × π × π × π × π and (π) means π π × π π × π π π × . π You have seen this kind of notation before, it is called exponential notation. In general, for any number π and any positive integer π, (π β π β― π) ππ = β π πππππ π The number π is called π raised to the π-th power, π is the exponent of π in ππ and π is the base of ππ . Exercise 1 Exercise 6 4×β―×4 = β 7 7 ×β―× = β 2 2 7 π‘ππππ 21 π‘ππππ Exercise 2 Exercise 7 3.6 × β― × 3.6 = 3.647 β (β13) × β― × (β13) = β _______ π‘ππππ 6 π‘ππππ Exercise 3 Exercise 8 (β11.63) × β― × (β11.63) = β 1 1 (β ) × β― × (β ) = β 14 14 34 π‘ππππ 10 π‘ππππ Exercise 4 Exercise 9 12 × β― × 12 = 1215 β π₯ β π₯ β―π₯ = β 185 π‘ππππ _______π‘ππππ Exercise 5 Exercise 10 π₯ β π₯ β― π₯ = π₯π β (β5) β × β― × (β5) = _______π‘ππππ 10 π‘ππππ Lesson 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Exponential Notation 1/4/17 S.1 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8β’1 Exercise 11 Will these products be positive or negative? How do you know? (β1) β × (β1) × β― × (β1) = (β1)12 12 π‘ππππ (β1) × (β1) × β― × (β1) = (β1)13 β 13 π‘ππππ Exercise 12 Is it necessary to do all of the calculations to determine the sign of the product? Why or why not? (β5) × (β5) × β― × (β5) = (β5)95 β 95 π‘ππππ (β1.8) × (β1.8) × β― × (β1.8) = (β1.8)122 β 122 π‘ππππ Lesson 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Exponential Notation 1/4/17 S.2 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 1 NYS COMMON CORE MATHEMATICS CURRICULUM 8β’1 Exercise 13 Fill in the blanks about whether the number is positive or negative. If π is a positive even number, then (β55)π is __________________________. If π is a positive odd number, then (β72.4)π is __________________________. Exercise 14 (β15) × β― × (β15) = β156 . Is she correct? How do you know? Josie says that β 6 π‘ππππ Lesson 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Exponential Notation 1/4/17 S.3 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 1 NYS COMMON CORE MATHEMATICS CURRICULUM 8β’1 Problem Set 1. Use what you know about exponential notation to complete the expressions below. (βπ) × β― × (βπ) = β π. π × β― × π. π = π. πππ β _____ πππππ ππ πππππ π × β― × π = πππ β π×β―×π = β π πππππ _____ πππππ (βπ. π) × β― × (βπ. π) = β π. π × β― × π. π = β ππ πππππ π πππππ ππ ππ ππ π (β ) × β― × (β ) = (β ) β π π π π π ( )×β―×( ) = βπ π ππ πππππ _____ πππππ (βππ) × β― × (βππ) = (βππ)ππ β π×β―×π = β π πππππ _____ πππππ 2. Write an expression with (β1) as its base that will produce a positive product. 3. Write an expression with (β1) as its base that will produce a negative product. 4. Tim wrote 16 as (β2)4 . Is he correct? 5. Could β2 be used as a base to rewrite 32? 64? Why or why not? Lesson 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Exponential Notation 1/4/17 S.4 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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