m n Use technology to discover the rules for forms such as a a, various integer values of m and n and a fixed integer value a.

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1 TIth.co Alger Expoet Rules ID: 988 Tie required 25 iutes Activity Overview This ctivity llows studets to work idepedetly to discover rules for workig with expoets, such s Multiplictio d Divisio of Like Bses d the Power of Power rule. Studets lso ivestigte the vlue of power whose expoet is zero or egtive. As optiol extesio, studets ivestigte the vlue of power whose expoet is frctio with uertor of oe. Topic: Polyoils Use techology to discover the rules for fors such s, vrious iteger vlues of d d fixed iteger vlue. Use techology to verify for vrious vlues of d tht iteger., d ( ) for = where is Evlute siple uericl expressios rised to itegrl expoets (icludig zero expoets). Use techology to evlute ore coplex uericl expressios ivolvig expoets. Techer Preprtio d Notes This ctivity is desiged to e used i Alger clssroo. It c lso e used i Pre-Alger clssroo, or y y studet lerig the rules for opertig with expoets. Studets should lredy e filir with sic powers, expoets, d ses, such s 2 3 = 8. While studets c use Scrtchpd t y tie, you y wish to review the positive powers of two efore egiig this ctivity (2, 4, 8, 6, 32, 64...). This ctivity is iteded to e ily studet-led, with reks for the techer to itroduce cocepts or rig the clss together for group discussio. Ech studet should hve his or her ow hdheld. Notes for usig the TI-Nspire Nvigtor Syste re icluded throughout the ctivity. The use of the Nvigtor Syste is ot ecessry for copletio of this ctivity. To dowlod the studet TI-Nspire docuet (.ts file) d studet worksheet, go to eductio.ti.co/exchge d eter 988 i the keyword serch ox. Associted Mterils ExpoetRules_Studet.doc ExpoetRules.ts 202 Texs Istruets Icorported Techer Pge Expoet Rules

2 TIth.co Alger Prole Discoverig expoet rules O pge.2, hve studets evlute the expressio i the lower left pe y selectig vrious vlues for d y ipultig the correspodig sliders. (Pressig /+e will llow studets to ove etwee pplictios i split widow.) TI-Nspire Nvigtor Opportuity: Scree Cpture See Note t the ed of this lesso. Hve studets work idepedetly o pge.3. Perfor Scree Cpture to check o studets progress. After copletig these two pges, ecourge studets to discuss their fidigs. Be sure tht studets oserve tht these rules pply oly whe the powers hve like ses. Verify tht studets hve checked the rule for pge.2, = +, d tht it is clled the Product of Powers rule. Propt studets to coclude tht the rule for pge.4, =, is the Quotiet of Powers rule. Note: For coveiece, the vriles d will e used whe expressig the Expoet Rules o the questio pges i this docuet. Becuse of the use of sliders i this ctivity, severl other vriles were used o the explortio pges. 202 Texs Istruets Icorported Pge Expoet Rules

3 TIth.co Alger Repet siilr process for the rule o pge.6, ( ) =, kow s the Power of Power rule. Studets cotiue workig idepedetly through pges.8 to., which llows the to explore egtive d zero powers, respectively. Be sure they drw the correct coclusios, 0 ely tht = d = (for 0 d positive iteger). Note: If studets re hvig difficulty tryig to fid frctio represettios of their decil results o pge.8, they y fid it helpful to chge their clcultor s settigs to llow for this. This c e doe y selectig c > Settigs > Docuet Settigs d chgig Clcultio Mode to Exct. Next, select Mke Defult. O pge.0, it is iportt tht studets 0 oserve 0 is cosidered udefied y the clcultor. TI-Nspire Nvigtor Opportuity: Quick Poll See Note 2 t the ed of this lesso. 202 Texs Istruets Icorported Pge 2 Expoet Rules

4 TIth.co Alger Studets fiish the ctivity y copletig pges.2 through.5. Pge.2 hs studets explore the Power of Product rule: ( ) = wheres o pge.4 they explore the Power of Quotiet rule: 0. =, where Agi, o pge.4, studets y fid it helpful to hve their hdheld s Clcultio Mode set to Exct. Prole 2 Extesio: Rtiol Expoets with Nuertor of Pge 2. sks studets to evlute the five expressios show to ke cojecture for They will see tht x = x. You y eed to expli tht whe = 2, the 2 is usully oitted: 2 =. x. TI-Nspire Nvigtor Opportuity: Quick Poll See Note 3 t the ed of this lesso. 202 Texs Istruets Icorported Pge 3 Expoet Rules

5 TIth.co Alger Note Prole, Scree Cpture This would e good tie to do scree cpture to verify studets re ipultig the sliders correctly d euverig through the docuet t resole pce. Note 2 Prole, Quick Poll You y choose to use Quick Poll to ssess studet uderstdig. You y sk the studets to evlute Note 3 Prole 2, Quick Poll You y choose to use Quick Poll to ssess studet uderstdig. You y sk the studets to evlute 3 25 or write equivlet expressio i rdicl for for 5 x. 202 Texs Istruets Icorported Pge 4 Expoet Rules

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