MATH IS FUN!!!MATH IS FUN!!!LetLets start by reviewing s start by reviewing exponent laws!exponent laws!Try TheseTry These(Do them on a sheet with your name and (Do them on a sheet with your name and the date they will be collected next class!)the date they will be collected next class!)impli!y"impli!y"#"#"($($% %)($)($& &))%"%"(&(&$ $)(&)(&' ')(&)(&% %))$"$"(((($ $)(())(())ultiplying powers )ultiplying powers *! you are *! you are multiplyingmultiplying powers with the same powers with the same base base $$& & x $x $+ +(here both numbers have a base o! $)(here both numbers have a base o! $)Then you ,eep the base the same and Then you ,eep the base the same and -DD-DD the the exponentsexponents$$& & x $x $+ + . $ . $ (& / +) (& / +)

. $. $#0 #0Dividing powers Dividing powers *! you are *! you are dividingdividing powers with the same powers with the same base base ''( (''$ $Then you ,eep the base the same and you Then you ,eep the base the same and you 12T3-4T12T3-4T the exponentsthe exponents''( ( 55 ''$ $ . ' . ' (( 6 $) (( 6 $)

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,,8xponents o! exponents 8xponents o! exponents *! you have to *! you have to simplifysimplify a power o! a power a power o! a power with the same base with the same base (%(%( ())$ $Then ,eep the base the same and Then ,eep the base the same and )1LT*9L:)1LT*9L: the exponentsthe exponents(%(%( ())$ $ . %. %(x$ (x$

. %. %#( #(Do these on your page Do these on your page 8xpress as a single power"8xpress as a single power"#"#"(#0(#0$ $))% %%"%"(%7(%7#$ #$))0 0$"$"(+(+6# 6#))6# 6#ometimes exponents o! ometimes exponents o! exponents can get tric,y!!exponents can get tric,y!!;hat happens when there are ;hat happens when there are variables in the we -DD-DD the the exponents> so exponents> so (x(x2 2 xx xx4 4) ) xx (y(y3 3 xx yy2 2) = (x ) = (x 2 + 4 2 + 4)(y )(y 3 + 2 3 + 2))

= x= x6 6yy5 5Do these on your page Do these on your page impli!y"impli!y"#"#"(w(w6+ 6+)(w)(w6' 6'))%"%"(x(x& &))% %$"$"hh67 67

hh6? 6?((xx2 2yy3 3))3 3*n this case> the $ outside the brac,et must apply *n this case> the $ outside the brac,et must apply to to 8@83:TA*BC8@83:TA*BC inside the brac,et!inside the brac,et!((xx2 2yy3 3))3 3 = (x= (x2 2yy3 3)(x)(x2 2yy3 3)(x)(x2 2yy3 3))This is Dust li,e the last example!This is Dust li,e the last example!E3E3;e ,now that when we want to ;e ,now that when we want to simpli!ysimpli!y the power the power o! a power> we o! a power> we )1LT*9L:)1LT*9L: the exponentsthe exponents((xx2 2yy3 3))33 = (x= (x2x3 2x3)(y)(y3x3 3x3))

. x. x+ +yy? ?Do these on your page Do these on your page impli!y"impli!y"#"#"(x(x( (yy% %))$ $%"(mp)%"(mp)& &(m(m( (p)p)$"(t$"(t$ $ww? ?)(t)(t% %))( (2ut what i! there are numbers and 2ut what i! there are numbers and variables===variables===(6x (6x% %) )#00 #00The exponent must still be applied toThe exponent must still be applied to 8@83:TA*BC 8@83:TA*BC insideinside the brac,et! the brac,et!(6x (6x% %) )#00 #00is the same as is the same as (6 (6# #x x% %) )#00 #00*n this case> the #00 applies to the 6# -BD the x *n this case> the #00 applies to the 6# -BD the x% %(6 (6# #x x% %) )#00#00 . (6 . (6# #) )#00 #00(x (x% %) )#00 #00. # . #x x %x#00 %x#00. #x . #x%00 %00Do these on your page Do these on your page impli!y" impli!y"#"#" (6#0y (6#0y( () )& &%"%" ($m ($m% %) )% %$"$" ((h ((h( (m m$ $) )? ? remember the ? applies toremember the ? applies toeverythingeverything in the brac,ets (thein the brac,ets (the(> the h (> the h( ( and the m and the m$ $) )E,> now !or something a little bit E,> now !or something a little bit new!!!new!!!:ou ,now how to simpli!y expressions with :ou ,now how to simpli!y expressions with exponents> but sometimes you are as,ed exponents> but sometimes you are as,ed to evaluate them a!ter they are simpli!ied"to evaluate them a!ter they are simpli!ied"21T21T what do you do with a what do you do with a negative negative exponentexponent=!==!=($($6% 6%)($)($6# 6#));e ,now that when we ;e ,now that when we multiplymultiply powers with powers with the same base> we the same base> we -DD-DD the exponents the exponents ($($6% 6%)($)($6# 6#) . $) . $(6% / 6#) (6% / 6#)

. $. $6$ 6$Aow do we evaluate this==Aow do we evaluate this==$$6$ 6$-nytime you have a negative exponent> you -nytime you have a negative exponent> you can ma,e it into a positive exponent by can ma,e it into a positive exponent by putting a # over number!putting a # over number!$$6$ 6$ . . ##$$$ $

. . ##??LetLets see another one o! those s see another one o! those *! we have the !ollowingF *! we have the !ollowingF( (6' 6' remember weremember we 12T3-4T 12T3-4T thethe ( (6$ 6$ exponents exponents( (6' 6' . ( . ((6' 6 6$) (6' 6 6$) .( .(6& 6&( (6$ 6$Bow> we simply put ( Bow> we simply put (6& 6& under a #under a # #G #G( (&& (it becomes positive) (it becomes positive)-nd we can evaluate it as we would any positive exponent -nd we can evaluate it as we would any positive exponent # # .. # #( (& &+%(+%(Do these on your page Do these on your page Hrom page %$0 in your textboo,FHrom page %$0 in your textboo,FIuestions ?> #0 and ##(a> c> e)Iuestions ?> #0 and ##(a> c> e)3emember * will be collecting this wor, next class! 3emember * will be collecting this wor, next class! *! you have di!!iculty> review the slides and then *! you have di!!iculty> review the slides and then as, one o! your classmates to help you!as, one o! your classmates to help you!Jorge try it on your own !irst!!!Jorge try it on your own !irst!!!A-@8 - C38-T D-:!!!A-@8 - C38-T D-:!!!