ࡱ> -/, bjbj++ %GAA""<B$\+f:*******,T,/+1^++.**(* Fk)*,+0\+)//(**0++\+/" :   Class Notes on The Exponent Rules What is a POWER? When it comes to mathematics, we refer to a power as an exponential expression used for indicating the numbers of factors involved in multiplication. There are special rules for powers that will make solving questions in this course easier if we apply them correctly. You may have been exposed to these rules way back in the day....  What is a BASE? The base is the number that gets multiplied.  What is an EXPONENT? The exponent is the number that tells you the number of times to multiply the base. The Exponent Rules Rule #1: Multiplying Powers with the Same Base When multiplying powers with the same base you ADD the exponents. Example: a3 x a2 = a3 + 2 = a5 Rule #2: Dividing Powers with the Same Base When dividing powers with the same base you SUBTRACT the exponents. Example: a5  EMBED Equation.3 a3 = a5 3 = a2 Rule #3: When Raising Powers to Another Power When raising a power to another power you MULTIPLY the exponents. Example: (a4)2 = a4 x 2 = a8 Rule #4: Powers with a Negative Exponent Powers with a negative exponent can be written as a FRACTION with a POSITIVE exponent. Example: a-5 =  EMBED Equation.3  Conversely, a fraction whose denominator has an exponent can be written as a power with a NEGATIVE exponent. Example:  EMBED Equation.3  = a-9 Rule #5: A Power with an Exponent of One When evaluating a power with an exponent of one, the answer will be the base. Example: a1 = a Rule #6: A Power with an Exponent of Zero When evaluating a power with an exponent of zero, the answer will be one. Example: a0 = 1 "#-2345afm A B пвХohXhXhn#hn#56OJQJ^J hn#5\jhn#CJUmHnHu"jhn#CJUmHnHsH uhn#h@,hn#5OJQJ\^Jh@,hn#OJQJ^Jhn#6OJQJ]^J!h@,hn#56OJQJ]^Jh@,hn#6OJQJ]^Jh-L6OJQJ]^J#h-Lh-LCJ OJQJ]^JaJ "#45  !gdn#gdn#$a$gd-L U V   _ ` gd-L$a$gd-L $ a$gdn# gdn#gdn#gdn#  !gdn#B U V ^ p q   ` 鲞wffVh-Lhn#56OJQJ^J h-L56CJOJQJ^JaJ#h-L56CJH*OJQJ^JaJ)hn#hn#56CJH*OJQJ^JaJ&hn#hn#56CJOJQJ^JaJhn#hn#56OJQJ^JhsB*aJ phh-Lhn#B*aJ phh-Lhn#5B*\aJ phhn##hu.hn#5CJOJQJ^JaJ` j k l m 줊yygycK/h-Lhn#5B*CJ OJQJ\^JaJ phh-L#h-L56CJH*OJQJ^JaJ h-L56CJOJQJ^JaJ3jh-Lh-L56CJEHOJQJU^JaJ5jR h-Lh-L56CJOJQJUV^JaJ/jh-Lhn#56CJOJQJU^JaJ)h-Lhn#56CJH*OJQJ^JaJ&h-Lhn#56CJOJQJ^JaJ     ! & + - / 0 8 9 X Y Z ϾτiP:P+hsB*CJ OJQJ^JaJ mH phsH 1h-Lhn#B*CJ OJQJ^JaJ mH phsH 4h-Lhn#5B*CJ OJQJ^JaJ mH phsH hn#OJQJ^JmH sH ,h-Lh-L56CJH*OJQJ\^JaJ)h-Lh-L56CJOJQJ\^JaJ!h-Lh-L56OJQJ\^Jhn#OJQJ\^Jh-Lhn#B*CJ aJ ph,h-Lhn#B*CJ OJQJ\^JaJ ph - . / 0 Y Z H I r s t u v w $a$gds$a$gd-Lgdn#gd-LZ |^I1.h-Lhs56CJOJQJ^JaJmH sH (h-L56CJOJQJ^JaJmH sH ;jh-Lh-L56CJEHOJQJU^JaJmH sH jR h-LCJUVaJ7jh-Lh-L56CJOJQJU^JaJmH sH 1h-Lh-L56CJH*OJQJ^JaJmH sH .h-Lh-L56CJOJQJ^JaJmH sH &h-Lhn#56OJQJ^JmH sH &h-Lh-L56OJQJ^JmH sH  G H I R S f g h i o r w ĶsU<1hshs56CJH*OJQJ^JaJmH sH ;j hshs56CJEHOJQJU^JaJmH sH jR hsCJUVaJ7jhshs56CJOJQJU^JaJmH sH .hshs56CJOJQJ^JaJmH sH hn#OJQJ^JmH sH &hshn#56OJQJ^JmH sH &hshs56OJQJ^JmH sH &hsh-L56OJQJ^JmH sH  w  ./zɸ{pbhn#OJQJ^JmH sH hsOJQJ\^J!hshn#56OJQJ\^J,hshs56CJH*OJQJ\^JaJ)hshs56CJOJQJ\^JaJ!hshs56OJQJ\^J hn#5\,hshn#B*CJ OJQJ\^JaJ ph/hshn#5B*CJ OJQJ\^JaJ ph ./yzgdn#$a$gds,1h/ =!"#$% n;1ǜWEr"A6jPNG  IHDR0XiPLTE/@@@4cW4<- ```}sVI000 pppǚ@@I;@@pe00PPP``ర ǚMg AppPP``>ZΧ00ճNgpp\tk?ZzPP1M/M"A]tΧڧճl{,e_tRNS_,bKGD^a cmPPJCmp0712HsgIDATx^{! )%dS7uӳ-{fdbX`g Ȓ,i:G&cEI`E-DGȨ=ᑙmT^AiA5! #╙Ug^/)&DHd0!4:\Lsf0*L%Ƥ6Pߓ""ĬiH :g1%)|B| !-u E%b#3#qyc$k&lwb4 SҮLA[A0NSHۖ%` Qjly`wSN:gc^fI+$&"o:k TTN!@1 pg傤J2i0bt`s^3$5 DJ݂G^9Ea}4d=Sٝ2B%;k|'B;0]Ѷ}5t.`(0P,Y PALW&ªg7 ^_+&JwEN)c^bYz#ԂcStN f £_wt .zCKi^[@k/~m\>@`d6\[օmlɼt9SUm]x{R0,Bl=Md?q$Jq+حPEzF>.ט6bmJ^̅/AU%u͊`͊Qv& "m"v6F]tNԐ5%,imK㔑®hTKyyyy{?j6.R?:wGGGw[Q72oʘk5j](DR(`XΡ@ASas:l.9UMځ+\d1vtR.5)MQwZdG"j!!z%mFu\\do$zsa*Hzb50ifa?F!pR A"m+M*N:Ѩ QHq#K!/ћ ".>@3 A Q-ئ_TM4þ")lⲄ*7 .l!(@ {i8rmm:xKq*h싧7r4ړ:[1}v #/'J,`/(iqx-#UhIni-^f8_dh1R.k3\_ڞ -iՓ֦KPךzyXֻE(Iɤ;LAXpMեvth"Ή\)J.tWB¨!f{gL+-.Uڜ4KͥQ42eU\֐vj{"x:\R/5a{jGpi/%ޭyAh''eЛ (7EWUscTkə<+V*ǯ!Z\5K1TJ@= trKf3^+k t# ERV]u2cZ[`O\FCåż"f֪ŌBwp3D|1Se;NQY˕J1t.]4cYUoUj4"|"7g{7hFrM\x亂BJ‹T&jqEQ7ס _H$@Dn(VYR-pDֲ)bq?L'Y,Ӓ\!f_Iǀɥ\[qsc>WȽɥVݢ]\ĆȈ=E\Vu͋K\ĽJ~ hl4K|S{E(Lχݛ\Ȍyq1S(W\(]5/nqQK8NiOUScg@A! R;*XOLqyZ}`nq(W+)iԁutk"ԳRg(ⵗAS)F 1W+ZXT"*pQyB֕h( {ߵ\`l\ܸbu{u0^u\ .o\v`"m+sjq1Bg]|΁7վ~\67Uדz˧C.Garqs?ښ{-Vÿ**|O l*O.uxථ%qfAcv:#V9~ZG ~ Nd֏᜔}ٔwٕ'7_Z|:^c`GsPx\76vH5x<ߎClх&t+c_ /ޟlYvIs7._t:Bgwd|=i#.N+rSK",[-VsZevO\|yFFjui.'錏D"<9t%AfXح~|)h싅/zT.вB5v:M\V Gp#os>ڳ((ZWP?83&=b}tlr3}*o4 B.h?=}[&fˍnGC-vW4T 膍w]Ûۀylyje!0%xuBd_l qQɋ|<.;/R /pb~os#paG.Pz;Wx>B'GjbﱱP?= ^› ݡix}&fvj[PeU>G4~_\u>x!iaGiYj([hG˗z`}Z>NP!=񨳒,vBD<. ңrQ?59K9i[]P]qseT7i{4=OW->͍zMRˢ3F݃]쟉giD` |r`={Bځk2 XKf'n;3PmC@@X\sn@o5:bO &@Kr3v`V/Rgx}]5րrЄ⢈(eqr;p^nXEezF=X\N^FrwSRYniq30n"t(E @&>$="-|,r/Q]{wqp7嗀e?i ^Љ ~K~F.owq#resbn.AEo}!~v,]q]$=ED3&v p=v[Yʰ/Ix.cwfxER _DBw~/\F!ulK.'Mw#~@+㍾ߔ1Z7/jC.j.sIENDB`FƊBԬvJFIFC    &"((&"%$*0=3*-9.$%5H59?ADED)3KPJBO=CDAC A,%,AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA^t"5!1AQa"2q#BR3b$!1"A#2Qa ?$JK&#Cx3*^aMϣ}e^۶26xhMs.ƜaY.jَ{qx8%y8>JZ8 siYFYᕪӕ! 4 !!@B!V7Nq"&S|NEi4&G;iǩ+Ե P4aJ0q^SW4;32" z%{:6N٥e0`܎v%b4NGzvqCO?\KbZ^t^}#ϲ:7I܁AJk;NÀ=׿uVmJ#F OB˔Y[b`7wRU,es[];gWPa{`'S0վH&"" !BG%b:>,R 9LMx MB9F[]m=Gp3E&خ0 wF^`c\ 9,Ԏi*ӋweMl/5ZP\u]Eao'^r#!ddaZx?LE).ZiP^?:eU\״9w9TS#nUdӺCVS&n3${P% a"AT9emqFB\#[> 2c;~14 ,9NK[wH9eA᭭ztxw}tT):gZ1'*dkS),ZOARr1cyFTs M1ɂ FxyU_whN}K;;1ɸhJXD$IZZAi,֎ahdo?G>Y=yBT PjJŪ7sX@R7!pƼaj vj֖.-&^ /Y-qp$=}VF9&3ZZ=ߺRj^"@0$aÿqi|7[PGS-p;5cdҙ7˽ا&Ř$3UZF-rnUW|##eg\V2Ss2[ܮӭ}W6W#]8{P=o&L.X潁!p#BR P%B )jE',>d$nzӽ|B\JװkA+Eu8ǹ0 ڤ/7I'j_?˩_U yRb; `aB]#=e UU-[Pl˚=!_!d`Dd \  c $A? ?#" `28O Ҙ@~D`! O Ҙ@~:@@x=Na{U" : ZRC $$rZxBx"*:d3,! X;̋K(Ba*jP!e,{+ȣЈ? ,2&`9Pz&c L}."UvDXuJzL z oNnXqTQq.&??Q5^$Dd hl\  c $A? ?#" `2t"ujhL b8])Y;P,`!H"ujhL b8])Y;@|xcdd``f 2 ĜL0##0KQ* WفIRcgbR vx@3zjx|K2B* Rj8 :@u!f0109Y@F;3)V ZZǰc@.W+LF]F\ϙ~3?@ABCDEFGHIJKLMNOPRoot Entry F/ 0 Data $WordDocument%GObjectPool / . _1388307954F  Ole CompObjfObjInfo  !"#% FMicrosoft Equation 3.0 DS Equation Equation.39q ,!  FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native )_1388308480 Fj  Ole CompObj fObjInfo Equation Native  C_1388308646F $ Ole  ',! 1a 5 FMicrosoft Equation 3.0 DS Equation Equation.39q',! 1a 9CompObj fObjInfoEquation Native C1Table9/ Oh+'0  , P \ ht|'$Class Notes on The Exponent RulesUser Normal.dotm Amy Bessen2Microsoft Macintosh Word@F#@t @t SummaryInformation(DocumentSummaryInformation8CompObj$` ՜.+,D՜.+,h$ hp  ' Toronto District School Board  "Class Notes on The Exponent Rules Title$ 8@ _PID_HLINKS'A]  exponent-BENwjPencilwjPencil F Microsoft Word 97-2004 DocumentNB6WWord.Document.86666666662 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH @`@ n#NormalCJ_HaJmH sH tH H@H n# Heading 5$@&CJ OJQJ^JtH DA D Default Paragraph FontRiR  Table Normal4 l4a (k (No List 8@8 n#Header  !tH PK!pO[Content_Types].xmlj0Eжr(΢]yl#!MB;.n̨̽\A1&ҫ QWKvUbOX#&1`RT9<l#$>r `С-;c=1g~'}xPiB$IO1Êk9IcLHY<;*v7'aE\h>=^,*8q;^*4?Wq{nԉogAߤ>8f2*<")QHxK |]Zz)ӁMSm@\&>!7;wP3[EBU`1OC5VD Xa?p S4[NS28;Y[꫙,T1|n;+/ʕj\\,E:! t4.T̡ e1 }; [z^pl@ok0e g@GGHPXNT,مde|*YdT\Y䀰+(T7$ow2缂#G֛ʥ?q NK-/M,WgxFV/FQⷶO&ecx\QLW@H!+{[|{!KAi `cm2iU|Y+ ި [[vxrNE3pmR =Y04,!&0+WC܃@oOS2'Sٮ05$ɤ]pm3Ft GɄ-!y"ӉV . `עv,O.%вKasSƭvMz`3{9+e@eՔLy7W_XtlPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-!pO[Content_Types].xmlPK-!֧6 -_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!!Z!theme/theme/theme1.xmlPK-! ѐ'( theme/theme/_rels/themeManager.xml.relsPK]# &B ` Z w    lRfh:::/Xb$;1ǜWEr"A6j.&R$ƊBԬv"@@(  v  C 2Aexponent-BEN#" ?d  C &APencil"?d  C &APencil"?B S  ?$ ?lN t0_Lt0GLtkqRiko:::::z*q"X;T,^@MEF@FK0tp_J{&X~Oh 88^8`hH.h^`.h L ^ `L.h  ^ `.hxx^x`.hHLH^H`L.h^`.h^`.hL^`L.h 88^8`hH.h ^`hH.h  L ^ `LhH.h   ^ `hH.h xx^x`hH.h HLH^H`LhH.h ^`hH.h ^`hH.h L^`LhH.h^`.h^`.hpLp^p`L.h@ @ ^@ `.h^`.hL^`L.h^`.h^`.hPLP^P`L.h ^`hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.h 88^8`hH.h ^`hH.h  L ^ `LhH.h   ^ `hH.h xx^x`hH.h HLH^H`LhH.h ^`hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.h 88^8`hH.h ^`hH.h  L ^ `LhH.h   ^ `hH.h xx^x`hH.h HLH^H`LhH.h ^`hH.h ^`hH.h L^`LhH.z*MEX;T,0tX~J{FK                                                               '<n#$-Ls@ʔWp@UnknownG*Ax Times New Roman5Symbol3 *Cx ArialA$BCambria Math"1h g g  !24 3QHP ?n#2!xx ,!Class Notes on The Exponent RulesUser Amy Bessen(