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MODUL 6
INDICES
1. Multiplication of numbers in index
notation.
i. Simplify
a
45 47
b
(6)3 (6)9
c
a5 a6 a7
d
3x4 5x6
e
m6n7 m3n5
f
3ab2 (a2b3)5ab2
ii. Simplify
a
x3 x4 x5
b
4a3 5a2
c
3p5 4p2 2p7
d
8b5 a2b3 2a3b2
e
3x3y4 4x2y3
iii. Simplify
a
24 35 36 23
b
71183 710 83 82
c
34 105 114 103 32 115
d
124 75 74 123 123
2. Division of numbers in index
notation
i. Simplify
a
39 33
b
117 112
c
2317 235
d
126 12
e
716 710
f
1010 1010
ii. Simplify
a
p6 p5
b
x19 x12
c
x7y6 x3y2
d
r7s6t3 r2s4t2
iii. Simplify
a
20d5 (2d2)
b
36e7 4e3
c
121e9 f 6 11e6 f 2
am an amn
am an amn
d
625p7q6r5 25p4q3r4
3. Raising numbers and algebraic
terms in index notation to a power.
i. Simplify
a
(32)5
b
(43)4
c
(53)7
d
(135)3
e
(116)6
ii. Simplify
a
(p3)5
b
(m6)3
c
(n10)9
d
(q4 )6
iii. Simplify
a
(33 54 )2
b
(26 73)4
c
(23 34 53)3
d
(63 75 117)4
iv. Simplify
a
(ab2)3
b
(3x2y3z4)3
c
(5x3y)2
d
(3x4z5)2
v. Simplify
a
a14
a6
2
b
16x13
2x 6
3
c
10p6q7
5p2q4
2
d
8s8t 5
(2s2t)3
e
(3x2y3)2 (2x3y)3
6x5y2
f
(9p6q2)2
(p2q3)3
g
6a5b3c 2
2ab2c 3
0
4. Negative indices
(am)n amn
(am bn )p (amp bnp)
am
bn
p
amp
bnp
an 1
an
i. Write each of the following with a
positve index
a
54
b
79
c
2
3
5
d
p10
ii. Rewrite each of the following with a
negative index
a
1
116
b
1
85
c
1
c11
d
1
xm
e
6
y 7
f
1
5r5
iii. Simplify each of the following.
a
(66 63 65)2
b
75 72 73
c
5
x3
2
d
2a3b2
3a2b
2
e
65 64 68
f
94 93 (93)2
5 Fractional indeces
i. Express the following as radicals
using the root signs.
a
101
2
b
31
4
c
91
3
d
p1
7
ii. Express the following as powers
a
53
b
115
c
q7
a1
n an
iii. State each of the following in the
form of (i)
(am )1
n and (ii)
(a1
n )m
a
72
3
b
153
4
c
262
5
iv. State each of the following as a
radical in the form of (i)
amn
and
(ii)
( an )m
a
93
5
b
102
7
c
135
9
v. Simplify each of the following
a
64a33
b
27p6q9
c
(x4y 6z8)1
2
d
9y 6z4
25x 8
1
2
vi. Simplify each of the following.
a
82
3
b
813
4
c
100 0003
5
d
3432
3
e
3432
3
vii. Simplify each of the following
a
272
3 32 811
4
b
163
4 645
6 82
3
