5indices1
TRANSCRIPT
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INDICES
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23= 2 x 2 x 2
2.5 x 2.5 x 2.53
4
62
5 x 5 x 5 x 5 x 5 x 5 x 5
87
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Indices
is read as 3 to the power
of 4 where 3 is the base
and 4 is the inde!
4
3
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Repeated Multiplication63" 6 6 6
2#" 2 2 2 2 2
$%&'4" $%&' $%&' $%&' $%&'
$3y'3" $3y' $3y' $3y'
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Repeated Multiplication9 9 9 "
2# 2# 2# 2# 2# "
$%(&' $%(&' $%(&' $%(&'"
$6w' $6w' $6w' "
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By using te calculato! "ind te #alueso" te "ollo$ing indices
1! 6# "
2! $%12'4 "
3! $2!4'4 "
4! 1#3 "
#! $32!9'2 "
6! $)'# "
*! $%+' 4 "
! $-'4 "
9! $./3'3 "
10! $#0'4 "
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Exp!essing a ce!tain nu%&e! in teindex notation.
Eape 1 Epress 32in the inde notation
with base 2!
2 322 16
2 2 42 2 1
2#
Eape 2 Epress 62# in
the inde notationwith base
#!
# 62## 12#
# 2## # 1 #4
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Exe!cise Epress eah of the foowin& in the inde notationwith the base &ien in the bra(ets
1! 16 $base 2'
2! 1 $base 3'
3! 64 $base 2'
4! 12# $base #'
#! 2#6 $base 4'
6! 243 $base 3'
*! 216 $base 6'
! 343 $base *'
9! 12 $base 2'
10! 10 000 $base 10'
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M'()I*(IC+)I,N ,-
N'MBERS IN INDEN,)+)I,N
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Exa%ple/
1! 32 33 " 3 3 3 3 3 "3# times5
33333
2! 93 94 "9 9 9 9 9 9 9 "9
*
times7
9999999
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Exa%ple/ 3! &4 " & & & & & & & & & "&9
times
ggggggggg
9
4! 1#1, 1#14 "
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0e!i"y a%x an= a%1n
1! #4 ## " #45# " #9
2! h11 h1" h1151 " h29
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Exe!cise
& 103E!#!27
1abdef2ab
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M'()I*(IC+)I,N ,-
N'MBERS ,R+(EBR+IC )ERMSI)4 )4E S+ME B+SE
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Exa%ple/1! 3a2 2a3" $32' a253 "6a#
2! 6f# 2f3" $62' f#53 "12f
3! 42 29" $42' 259 "11
4! 89 383" $3' 8953 "24812
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Exe!cise/1! 9d2 2d10" $92' d2510 "1d12
2! 10n4 2n3" $102' n453 "20n*
3! 4w2 w14" $41' w2514 "4w16
4! 819 3483" $134' 81953 "34822
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Si%pli"y %ultiplication o" nu%&e!s o!alge&!aic te!%s $it di""e!ent &ases
Exa%ple/
1! 32 23 342*" 3 254 "36 210 235*
2! (# 6 (,*"
3! $)'9 $)'4 $+'12$+'9"
( #5, "(13 13 65*
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Exe!cise
& 104E!#!2
1%10
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DI0ISI,N ,-N'MBERS IN INDE
N,)+)I,NMR REDZ
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0e!i"y a%an= a%6n
1! #*:## " #*%# " #2
2! h21:h1" h21%1 " h3
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Exa%ple/
1! 3# : 33 "
3! 99
: 94
"
2! (14: (# "
4! 1#1: 1#14 "
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Exe!cise& 106
E!#!37
1abdef2ab
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Exe!cise/1! 9d12:3d2" $9 :3' d12%2 "3d10
2! 10n4:2n3" $10 :2' n4%3 "#n1
3! 40w2*: 4w14" $40 :4' w2*%14 "10w13
4! 2#819: #83" $2# :#' Z19%3 "#816
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Exe!cise& 106
E!#!37
2def&h3abd
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R+ISIN N'MBERS+ND +(EBR+IC
)ERMS IN INDEN,)+)I,N
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0e!i"y 7a%8n= a%n
1! $#*'# " #*# " #3#
2! $h20'" h20 " h160
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3! $2*'# " *# " 2#3#
4! $32h'" h " 316h642
1#
32
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Exe!cise& 10
E!#!47
1%
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Exe!cise& 109
E!#!4
;uestion 1ony
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C,M*')+)I,NS
IN0,(0INNE+)I0E INDICES
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0e!i"y a6n=
1! %* "7
8
1
2! f%2 "2
1
f
n
a
1
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Exe!cise& 112
E!#!#7
1 7
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*ER-,RM C,M*')+)I,NSIN0,(0IN NE+)I0E INDICESEape
1! 2%2 2%4 " 2%25 $%4' " 2%2%4" 2%6
2! *%# : *%2 " *%# % $%2' "
*%#52
" *
%3
3! $%2'%4 " %2 $%4' "
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E xe!cise& 113
E!#!#
;uestion
1 %
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C,M*')+)I,NS
IN0,(0IN-R+C)I,N INDICES
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0e!i"y a = ( )m
n
an
m
n
m
a
power
root
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0e!i"y a =
1! + " ( )8
2! f - "
( )m
n
a
( )f
n
m
9 :
93
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Cange to !oot notation/
=2
1
25 =3
1
27
=5
1
32 =21
49
1!
4!
2!
3!
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Calculate te #alues using calculato!/
=2
1
81
1!
( )1
2 81
:.*!ess ;
5.*!ess :
?.*!ess =" 9
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=4
1
81
2!
( )1
4 81
" 3
:.*!ess 9
2.*!ess si"t >
3.*!ess :9.*!ess =
5.*!ess >?.*!ess :
@.*!ess =
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Exa%ple/ Calculate te #alues/
2
1
25 31
27
5
1
32 21
49
1!
4!
2!
3!
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Exe!cise& 11
E!#!6D
1 % 10
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Exe!cise& 11*
E!#!6=
1 2 3 # 6 *
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Exe!cise& 11*
E!#!6=
1 %