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Title: Mathematics - Indices
Description: A pdf which is ideal for teachers as a teaching aid in the teaching learning process. Students can master the lesson of Indices in Algebra. (Intermediate level) Consists of considerable amount of examples.
Description: A pdf which is ideal for teachers as a teaching aid in the teaching learning process. Students can master the lesson of Indices in Algebra. (Intermediate level) Consists of considerable amount of examples.
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MATHEMATICS
Index notation is used to write a number which is
multiplied repeatedly, in a concise way
...
That is, 2 × 2 × 2 = 23
...
2
3
32 = 3 × 3 = 9
54 = 5 × 5 × 5 × 5 = 625
22 × 3 = 2 × 2 × 3 = 12
62 × 52 = 6 × 6 × 5 × 5 = 900
4
43
22 × 32
216
73
63
74
33 × 52
6
3
3
Seven to the power three
5
16 = 2 × 2 × 2 × 2 = 24
16 = 4 × 4 = 42
6
Expressing a number in index notation with a prime
number as the base
7
25 = 5 × 5 = 52
64 = 2 × 2 × 2 × 2 × 2 × 2 = 26
81 = 3 × 3 × 3 × 3 = 34
49 = 7 × 7 = 72
8
2 18
3
3
9
3
1
2 24
2 12
2 6
3 3
3 45
3 15
5 5
1
2 72
2 36
2 18
3 9
3 3
1
3 63
3 21
7 7
1
1
18 = 2 × 3 × 3
= 21 × 32
63 = 3 × 3 × 7
= 32 × 71
24 = 2 × 2 × 2 × 3
= 23 × 31
45 = 3 × 3 × 5
= 32 × 51
72 = 2 × 2 × 2 × 3 × 3
= 23 × 32
9
Powers with an algebraic symbol as the base
10
11
(i) x4
(ii) a3
(iii) m3 × n3 = m3n3
(iv) 73 × p2 = 73p2
(v) 73 × y4 = 73y4
12
a2 = a × a
2p2 = 2 × p × p
23m2 = 2 × 2 × 2 × m × m
32x3 = 3 × 3 × x × x × x
x3y3 = x × x × x × y × y × y
13
Finding the value of a power by substitution
14
15
(i) x4 = x × x × x × x
=3×3×3×3
= 81
(ii) 3x2 = 3 × x × x
=3×3×3
= 27
16
(iii) 5x3 = 5 × x × x × x
=5×3×3×3
= 135
17
(i) 2a2 = 2 × a × a
=2×3×3
= 18
(ii) 22a2 = 2 × 2 × a × a
=2×2×3×3
= 36
18
(iii) 7a2 = 7 × a × a
=7×3×3
= 63
19
(i)
x2y3 = x × x × y × y × y
=1×1×7×7×7
= 343
(ii) 2x3y = 2 × x × x × x × y
=2×1×1×1×7
= 14
20
(ii) 3xy2 = 3 × x × y × y
=3×1×7×7
= 147
21
(i) a2b = a × a × b
=2×2×7
= 28
(ii) ab2 = a × b × b
=2×7×7
= 98
22
(iii) a3b𝟐 = a × a × a × b × b
=2×2×2×7×7
= 392
23
Title: Mathematics - Indices
Description: A pdf which is ideal for teachers as a teaching aid in the teaching learning process. Students can master the lesson of Indices in Algebra. (Intermediate level) Consists of considerable amount of examples.
Description: A pdf which is ideal for teachers as a teaching aid in the teaching learning process. Students can master the lesson of Indices in Algebra. (Intermediate level) Consists of considerable amount of examples.