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Monday, February 29, 2016

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INDICES

MR REDZ

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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

MR REDZ

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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

MR REDZ

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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

MR REDZ

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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 =

M d F b 29 2016

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Exa%ple/ Calculate te #alues/

2

1

25 31

27

5

1

32 21

49

1!

4!

2!

3!

M d F b 29 2016

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Exe!cise& 11

E!#!6D

1 % 10

M d F b 29 2016

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Exe!cise& 11*

E!#!6=

1 2 3 # 6 *

M d F b 29 2016

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Exe!cise& 11*

E!#!6=

1 %

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