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TheRulesOfIndicesRule1:Multi=………Rule2:DivisionofIndices anam=……Rule4:Forbersamn=…Rule3:Fornegativeindices a-m=……WhatIsAnIndeNumberYoushouldnowthat:888888=86Wesay“eighttothepowerof6”TheberTheorethanoneofindenumbersisindicesareindenumberswhicharepowersWhataretheindicesintheepressionsbelow:a354b36934c8372493&2ThenumbereightisthebasenumberMultiplicationOfIndicesWenowthat:77777777=78Butwecanalsosimplifyepressionssuchas:6364Tosimplify:1Epandtheepression=66666662Howmany6’sdoyounowhave73Nowwritetheepressionasasinglepowerof6=67eyResult6364=67Usingtheplifythefollowingepressions:13734=31128589=81434114748=426Wecannowwritedownourfirstruleofindenumbers:Rule1:Multi=anmNB:ThisruleonlyamonbasenumberWecannotsimbersWhatGoesInTheBo1Simplifytheepressionsbelow:164632979231161141491412527252730622232578781088520530550=67=99=117=1421=2755=210=818=5100DivisionOfIndicesConsidertheepression:Theepressioncanbewrittenasaquotient:NoweeratoranddenominatorHowmanyeightswillcancelfromtheto4Cancelandsimplify=83Result:8784=83Usingtheplifytheepressionsbelow:13932=37281186=853424413=411Rule2:DivisionofIndices anam=an-mWecannowwritedownoursecondruleofindenumbers:WhatGoesInTheBo2Simplifytheepressionsbelow:1595227127531961943615361051840182062322277870839852005180=57=77=195=365=1820=25=831=520NegativeIndeNumbersSimplifytheepressionbelow:5357=5-4Tounderstandthisresultfullyconsiderthefollowing:Writetheoriginalepressionagainasaquotient:Eeratorandthedenominator:Canceloutasmanyfivesaspossible:Writeasapoweroffive:Nowcomparethetworesults:Theresultonthepreviousslideallowsustoseethefollowingresults:Turnthefollowingpowersintofractions:(1)(2)(3)Wecannowwritedownourthirdruleofindenumbers:Rule3:Fornegativeindices:. a-mMoreOnNegativeIndicesSimbereachtime:(1)2WhatGoesInTheBo3Changetheepressionsbelowtofractions:Simberatalltimes:(1)(2)(3)(4)(5)(6)(7)PowersOfIndicesConsidertheepressionbelow:232Toappreciatethisepressionfullydothefollowing:Einsidethebracet=2222Squarethecontentsofthebracet=222222Nowwritetheepressionasapowerof2=26Result:232=26Usetheresultontheplifythefollowingepressions:(1)(42)4(2)(75)4(3)(87)6=48=720=842Wecannowwrite

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