# Unit 1: Chapter 4 Roots & Powers

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1 Unit 1: Chpter 4 Roots & Powers Big Ides Any number tht cn be written s the frction mm, nn 0, where m nd n re integers, is nn rtionl. Eponents cn be used to represent roots nd reciprocls of rtionl numbers. The eponent lws cn be etended to include powers with rtionl nd vrible bsed, nd rtionl eponents. Competency Focus: Communiction nd Representing Use mthemticl vocbulry nd lnguge to contribute to mthemticl discussions. Eplin, clrify, nd justify mthemticl ides. Lerning Outcome I cn demonstrte n understnding of powers with integrl nd rtionl eponents. Course Concepts I cn communicte my understnding bout concepts, procedures, nd problem solving strtegies s they relte to: Positive eponents Zero eponents Negtive eponents Frctionl eponents Rtionl eponents Self-Assessment Pre Post I cn pply the eponent lws to simplify epressions Vocbulry irrtionl number rel number

2 Nme: Due Dte: Assignment List Unit 1: Chpter 4 Roots nd Powers Section Pge #s / Question #s 4.2 pp #1 4, 9c, 10, 14, 15, 18, pp #1 8, 11, 12, pp.2 24 # 9, 1, 16, 18, pp # 6, 7 10 odd letters, 14 16, 21, 22 Review p.26 #1 8; pp #16-2 Reding Pge #s pp pp pp Completed / Checked Quiz Review p.249 #1 8; p.25 #19 25 Chpter Test Assignment: Red pp

3 Section 4.2 Irrtionl Numbers (pges ) Estimting Roots Emple 1: Estimte the following epressions: ) 64 b) 625 c) 27 d) e) 81 f) 0 g) 0 n th Root: nn The Rel Numbers The numbers in this system my be clssified s either rtionl or irrtionl numbers. Rtionl Numbers: numbers tht cn be written in the form of mm nn, where nn 0. Integers Proper frctions Improper frctions Terminting decimls Repeting decimls Irrtionl Numbers: numbers tht cnnot be written in the form of mm nn, where nn 0. Rdicls Specil vlues represented by symbols / vribles

4 Emple 2: Determine whether the following rdicls re rtionl or irrtionl. ) 8 b) 20 c) 52 d) e) 24 f) g) ππ h) 6 25 i) 27 Rel Number System Emple : Use number line to order these numbers from lest to gretest. 4.15, 15, 81 4, 25, 15 4 Assignment: pp #1 4, 9c, 10, 14, 15, 18, 21 Red pp

5 Section 4.4 & 4.5 (pges ) Frctionl Eponents nd Rdicls & Negtive Eponents & Reciprocls Review Eponent Rules bb +bb bb ( bb mm ) nn mmmm Rdicls cn lso be epressed s rtionl (or frctionl) power of n epression. It will sometimes be esier to use this new method of epressing rdicl to simplify rdicl epression. When you see rdicl epression, you cn convert it to frctionl power. Specificlly, n m n m OR in Generl: ( ) n m Notice: The inde of the rdicl becomes the denomintor of the rtionl power, nd the eponent of the rdicnd (epression inside the rdicl) becomes the numertor. Emple 1: Epress s frctionl eponents ) b) 9 c) d) e) f) Emple 2: Write the following in rdicl form then evlute ) 4 2 b) 16 4 c) 27 4 d) e) 49 2 f)

6 Remember the Rules of Eponents? They re still vlid for rtionl eponents!!! Emple : Eponent Rules ) 5 4 b) 4 5 b b b + b 1. Chnge to frctionl powers 2. Eponent Lws: Common Bse & Multiplied dd eponents i. Adding/subtrcti ng frctions must hve common denomintors ii. Add/subtrct numertors; leve denomintors b c) ( ) b ( ) 4 Multiplying Frctions: Numertor Numertor Denomintor Denomintor Eponentil Ptterns Emple 4 Power Epnded Form Numericl Vlue Power Epnded Form Numericl Vlue For ny non-negtive rel number nd ny positive integer, n

7 Emple 5: Write the following s positive eponent ) 2 5 b) 100 c) 7 Emple 6: Evlute ech power without using clcultor. Steps: 1. Reciprocte the power 2. Clculte vlue for the positive eponent. Evlute ) 5 b) 10 5 c) 7 2 d) 2 4 Emple 7: Evlute ech power without using clcultor. e) f) g) h) Assignment: pp #1 8, 11, 12, 17; pp.2 24 # 9, 1, 16, 18, 19 Red pp

8 Section 4.6 Applying the Eponent Lws (pges ) Emple 1: Write down the lw nd n emple to illustrte the eponent lw. Rule Emple Eponent of 1 1 Eponent of 0 0 Product Rule mm nn Quotient Rule mm nn ( mm ) nn Power Rules () mm bb mm nn Negtive Eponents bb nn mm nn Rtionl Eponents nn nn mm

9 Emple 2: Evlute the following without using clcultor. Stte the eponent lw(s) used. Eponent Lw(s) Used ) b) c)

10 Emple : Simplify. Epress without brckets or negtive eponents. Eponent Lw(s) Used d) (2 2 bb) e) ( 2 bb cc 4 )( 2 bbcc ) 2 f) 12 5 yy yy 1 2 g) 1 yy 4 2 yy yy Assignment: pp # 6, 7 10 odd letters, 14 16, 21, 22 *** QUIZ *** *****Chpter 4 Test on *****

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