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Transcript of ch3 Indices and Surds - WordPress.com · 186 Chapter 3 Indices an d su rds 1 Simplify using index...
Chapter 3 Indices and surds186
1 Simplify using index form.a 3 × 3 × 3 × 3 b 7 × 7 × 7 × 7 × 7 × 7c 8 × 8 × 8 d 2 × x × x × 3 × xe 3 × y × y × 5 × y × y f 2 × b × a × 4 × b × a × a
2 Copy and complete this table.
x 4 3 2 1 0
2x 23 = 8
3 Copy and complete.a 22 × 23 = 2 × 2 × ______ b x
x
x x x
x
5
3= × × ×
= −
____________ = 2−
c a a a
a
2 3( ) = × × ×
= −
______ ______ d ( ) ___ ___2 2
2
0 0x x× = ×=
Exercise 3F
Unde
rsta
ndin
gFl
uenc
y
4 Simplify using the first index law.a a a5 4× b x x3 2× c b b× 5
d 7 22 3m m× e 2 34 3s s× f t t8 82×
g 15
2p p× h 14
23
4 3c c× i 35
35
ss×
j 2 32 2x y xy× k 3 52 5a b ab× l 3 67 2v w v w×
m 3 5 104 2 4x xy y× × n 2 3 23 4 2 2rs r s r s× × o 4 56 7 2m n mn mn× ×
5 Simplify using the second index law.a x x5 2÷ b a a7 6÷ c q q9 6÷
d b b5 ÷ e yy
8
3 f dd
8
3
g jj
7
6 h mm
15
9 i 2 2 3x y x÷
j 3 5 2 3r s r s÷ ( ) k 6 34 2 2 2p q q p÷ ( ) l 16 87 5 3 4m x m x÷ ( )m
5 2 4
2a ba b
n 82
4
3stt
o 28
5
3vv
p 714
2a bab
q -3
9
4
3
x y
x y r
-8
16
2 3
2
x y
x y
Example 13
Example 14
ISBN 978-0-521-17866-2 Photocopying is restricted under law and this material must not be transferred to another party.
© David Greenwood, Sara Woolley, Jenny Goodman, Jennifer Vaughan, GT Installations, Georgia Sotiriou, Voula Sotiriou 2011 Cambridge University Press
Number and Algebra 187
Flue
ncy6 Simplify using the third, fourth and fifth index laws.
a x5 2( ) b t3 2( ) c 4 2 3a( ) d 5 5 3
y( )
e 4 2 3t( ) f 2 2 2
u( ) g 3 3 3r( ) h 3 4 4
p( )i
ab
2
3
2⎛⎝⎜
⎞⎠⎟
j xy
3
4
3⎛⎝⎜
⎞⎠⎟
k x yz
2 3
4
2⎛⎝⎜
⎞⎠⎟
l u w
v
4 2
2
4⎛⎝⎜
⎞⎠⎟
m 35
2 3fg
⎛⎝⎜
⎞⎠⎟
n 32
2
3
2a bpq
⎛⎝⎜
⎞⎠⎟
o atg
3
4
3
3
⎛⎝⎜
⎞⎠⎟
p 4
3
2 3 4p q
r
⎛⎝⎜
⎞⎠⎟
7 Evaluate the following using the zero power.
a 8 0x b 3 0t c 5 0z( ) d ( )10 2 0ab
e 5 3 3 0g h( ) f 8 50x − g 4 90b − h 7 4 20 0x y− ( )
Example 15
Example 16
Prob
lem
-sol
ving
8 Use appropriate index laws to simplify the following.
a x x x6 5 3× ÷ b x y xy xy2 2÷ ( ) ×
c x n x n xn4 7 3 2× ÷ ( ) d x y x y
x y
2 3 2 4
3 5×
e m w m w
m w
2 3 2
4 3×
f r s r s
r s
4 7 4 7
4 7×
g 9 6
12
2 3 7 5
6x y x y
xy×
h 4 12
24
2 3 2 2
4x y x y
x y×
i 16 4
32
8 7
7 6a b ab
a b×
j 3 2 4 3 2m n mn( ) ×
k -5 32 3 2a b ab( ) × ( ) l 4 32 2 2 4 2 3f g f g fg( ) × ÷ ( )( )
m 4 3
6
2 2 3
2
m n m n
m n
× ( ) n
7 3
7
2 2 2
2
y z yz
yz
( ) ×
( )
o 2 2
4 4
2 2 3
2 7 3
( ) ( )ab a b
ab a b
××
p 2
3
6
2
3 2
4 0
5 2
3 4
m
mn
n
n m
( )( )
×( )
( )-9 Simplify:
a (-3)3 b -(3)3 c (-3)4 d -34
10 Simplify:
a x2 3 2( )( ) b a5 3 7( )( ) c ab
2 3 5⎛⎝⎜
⎞⎠⎟
⎛
⎝⎜⎜
⎞
⎠⎟⎟
ISBN 978-0-521-17866-2 Photocopying is restricted under law and this material must not be transferred to another party.
© David Greenwood, Sara Woolley, Jenny Goodman, Jennifer Vaughan, GT Installations, Georgia Sotiriou, Voula Sotiriou 2011 Cambridge University Press