SModule 2: Integer ExponentsCollege AlgebraJerome A. Jimenez, MoMInteger ExponentsThe produt o! a and b an be "ritten asa . b #a$#b$ a#b$ #a$b abThe numbers a and b are alled !ators o! produt ab.Suppose "e ha%e the produt o! t"o !ators, eah being x. "e an use the notationx2 & #x$#x$'here the numeral 2 "ritten at the upper right o! the s(mbol is alled an exponent.Integer ExponentsIn general, i! a is a real number and n is a positi%e integer,an & a . a . a )a #n !ators o! a$'here n is alled the exponent, a is alled the base and an is alled the nth po"er o! a.*ote: "hen a s(mbol is "ritten "ithout an exponent, the exponent is understood to be +.Illustration2, & 2 x 2 x 2 x 2 x 2& -2#.-$- & #.-$ #.-$ #.-$& .2/Integer ExponentsTheorem +I! m and n are positi%e integers and a is a real number, thenan . am & an0mExample2- . 22 & 2-02 & 2, & -2x1 . x & x10+& x,Integer ExponentsTheorem 2I! m and n are positi%e integers and a is a real number, then#an$m & anmExample#2-$2 & 2#-$#2$

& 22& 21#x2$, & x#2$#,$& x+3Integer ExponentsTheorem -I! n is positi%e integer and a and b are real numbers, then#ab$n & anbnExample#2 . ,$- & 2- . ,- & 4 . +2, & +333#x2(1$, & #x2$,#(1$, & x#2$#,$(#1$#,$ & x+3(23Integer ExponentsTheorem 1I! m and n are positi%e integers and a is a real number "here a 5 3, thennama=nmanama=1nmanama=1Example5x5x=16x2x=62x=4x3x7x=173x= 14xInteger ExponentsTheorem ,I! n is a positi%e integer and a and b are real numbers "here b 5 3, thenabn= anbnExample523 =5253= 3224334x2z3y=34x2z( )33y( )=34x( )32z( )9y=12x6z9y6ero and *egati%e Integer ExponentsI! n is a positi%e integer and a is a real number "here a 5 3, thena3 & +a.n & +7anExample06=124= 124= 11605( )32( )=1132( )= 18Exerises