Indices worksheet

MODUL MATEMATIK PT3 TINGKATAN 3
NAMA : ____________________________________
+BAB 5 : INDEKS KELAS : ____________________
5.2 : PENDARABAN NOMBOR DALAM
TATATANDA INDEKS
CONTOH 1

(a)84 x 83 (b) k2 x k7 (c) 2p3 x 3p2
84+3 = 87 k2+7 = k9 (2 x 3) x p3+2 = 6p5

(a) 2² x 25 (b) (-5)8 x (-5)3 (c) 74 x 7 x 72

(d) p4 x p (e) 4m12 x 6m3 (f) -7n2 x 2n5 x (-n3)
(g) 4 x 43 x 46 (h) 24 x 23 x 22 (i) (-6)3 x (-6)2 x (-6) x (-6)7

(j) ( 4 )3 x ( 4 )2 x ( 4 )8 (k) (4.2)4 x (4.2)2 (l) n x n3 x n5
9 9 9

(m) 3p2 x 5p4 (n) 2k x (-6k3) x 4k2 (o) 5m5 x m2 x 3m3

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MODUL MATEMATIK PT3 TINGKATAN 3
(c) (-3)9 x (-3)4
LATIHAN 1

A. Permudahkan setiap yang berikut.
Simplify the following.

(a) 27 x 2 x 29 (b) ( 3 )2 x ( 3 )3
5 5

(d) (1.2)5 x (1.2) x (1.2)8 (e) -7h5 x 2h3 x 3h2 x h7 (f) 5 s4 x 4 s x 9s7
6 5

(g) 53 x 5 (h) (-2)4 x (-2) x (-2)2 (i) ( 3 )4 x 3 x ( 3 )5
4 4 4

(j) k3 x k x k5 (k) p x 6p3 x 3p 3
(m) 6r2 x 9r4 (n) 5j x (-7j3) x 2j2 (l) 5n3 x 10n4 x 4n
(o) 4w5 x 2w2 x 2w4

(p) 8u x u x ½u (q) 3b x 5b x 6b (r) 2t x t2 x 6t4

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MODUL MATEMATIK PT3 TINGKATAN 3

CONTOH 2 (a) 24 x 32 x 23

55 x 78 x 5 (c) (4.2)4 x (1.2)3 x (4.2)2
= 55+1 x 78 (e) k6 x h2 x k x h3 x k4
= 56 x 78
(g) 4x3 x ( − 1 2) x 2x x 3y4
(b) 5 x 43 x 42 x 55 2
1
(d) ( 2 )2 x ( 3 ) x ( 2 )4 x ( 3 )5
5 7 5 7 (i) p4 x 3 q3 x p x 8q2
1
(f) 2m2 x 5n4 x 3m4 x n
(l) 9r4 x 2s2 x 6 s2 x (-3r2)
(h) 3r2 x (-4s3) x ( − 1 4) x 2s2
3

(k) (-6k6) x (-2h4) x h8 x k4

3

MODUL MATEMATIK PT3 TINGKATAN 3

LATIHAN 2 (b) (1)6 x (52)8x (1)7 x (2)2

B. Permudahkan setiap yang berikut. 3 3 5
Simplify the following.
(a) (0.7)3 x (0.9)5 x (0.7)9 x (0.9)3 (f) a9 x 2a x 3a x 4b2 x b

(e) ( 1 )7x ( 1 )9x ( 1 )5x ( 1 )7 (h) ( − 3 8) x (-5f4) x 2e2
10
1
(g) 4b2 x 8 c6 x 6b x c2 (j) 87 x 64 x 83 x 6

(i) 24 x 33 x 22 x 35

(k) m5 x n9 x m3 (l) 5p6 x 3q9 x p x 2q2
1
(n) 5m6 x n x n5 x (-3m)
(m) 8k2 x 2h7 x 6k x (-3h2)

4

MODUL MATEMATIK PT3 TINGKATAN 3
(a) 312 ÷ 34
5.3 : PEMBAHAGIAN NOMBOR DALAM (d) 42v8 ÷ 7v7
TATATANDA INDEKS (g) (-63p14) ÷ (9p14)
CONTOH 3

(a) 88 ÷ 82 = 88-2 (b) g18 ÷ g6 = g18-6
= 86
(53)10÷ (3)6
(b) m15 ÷ m5
5
(c)

(e) (-6h12) ÷ 24h9 (f) (-3y5) ÷ (-3y4) ÷

(h) k15 x k5 (i) (- p )11 ÷ (- p )7 10
(k) 36x4 ÷ 9x2 (l) 12y9 ÷ (-6y3)
(n) 20n3 ÷ 4n (j) 6
27 ³
(o) 9 24 8

(m)

4

(p) 28r9s5 ÷ 7r4s5

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MODUL MATEMATIK PT3 TINGKATAN 3
(c) (-6)12 ÷ (-6)4
LATIHAN 3

A. Permudahkan setiap yang berikut.
Simplify the following.

(a) 78 ÷ 72 (b) 46 ÷ 45

2³ 5² (f) 311 ÷ 37 ÷ 3
(d) 2² (e) 5 (i) g15 ÷ g5
(g) 68 ÷ 62 (h) d7 ÷ d4

(j) y8 ÷ y4 (k) (-m)12 ÷ (-m)5 (l) 8r9 ÷ 4r5

(m) 48p7 ÷ 6p5 (n) 24q11 ÷ (-4q5) (o) 18m6 ÷ 6m2

(p) k15 ÷ k15 (q) -12n14 ÷ -4n6 (r) -42h16 ÷ 7h4

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MODUL MATEMATIK PT3 TINGKATAN 3
(a) (53)2
5.4 : NOMBOR DAN SEBUTAN ALGEBRA DALAM (d) ( 2)7
TATATANDA INDEKS YANG DIKUASAKAN
CONTOH 4

(a) (22)5 (b) ( 3)4 (c) [(− )4]2
22x5 = 210 x3x4 = x12 (-d)4x2 = (-d)8

(b) (87)3 (c) [(15)12]0

(e) ( 8)2 (f) [(2)3]5 (g) (-m6)0
(h) [(−7)5]2 (j) ( x8)3
5 (m) ( q5)5
(k) ( y4)6
(i) [(− )4]6

2

(l) ( z9)0

(n) [(− )10]2 (o) ) [(−ℎ)3]7 (p) (k5)5

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MODUL MATEMATIK PT3 TINGKATAN 3
(c) (73)6
LATIHAN 4 (f) (33)5
(h) [(−5)6]2
A. Permudahkan setiap yang berikut. (k) [(−11)³]4
Simplify the following. (n) [(−ℎ)²]9
(q) [(− )²]6
(a) (54)3 (b) (135)2

(d) (m2)7 (e) (p8)4

(f) (69)4 (g) (112)7

(i) [(−10)8]0 (j) [(−12)2]8

(l) [(− )²]8 (m) [(−t)²]3

(o) [(− )²]7 (p) [(− )²]3

8

MODUL MATEMATIK PT3 TINGKATAN 3

CONTOH 5 (c) (3hk4m2)4 =
34 x h4 x k4x4 x m2x4
(a) (25)4 x (53)2 = (b) ( 53)7 = = 81h4k16m8

25x4 x 53x2 = 220 x 56 = 5 7 35 (c) (− 2 2 8)4
(a) (156 ÷ 27)3 21
3 7

(b) e4 x ( 2 3)5

(d) (1 3 (e) (3 6 5)3 x 2vw4 (f) (2 3 6)3 ÷ 8( 5 4)2

2 5 4)

(g) (7552)4 (h) (2 53)5 (i) (23 42)4
(k) (6 42)2
(j) (32ℎ 42)2 (l) ( 2 4)4
(n) (−4 2 3 4)3 (o) (35 × 72 × 104)2
(m) (8 6)5

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MODUL MATEMATIK PT3 TINGKATAN 3
(c) (33 × 52)2x (23)2
LATIHAN 5

B. Permudahkan setiap yang berikut.
Simplify the following.

(a) 38 x 76 ÷ 75 = (b) pq x q5 ÷ pq5 =

(24)3× 85 ( 2 6)3 ( 2ℎ5)3

(d) 29 (e) 6 7 (f) ( ℎ2)6

136 5 7 (h) (4 2ℎ5)3÷ (2 ℎ2)4 (i) (3 3 )2 x 2pq2 x (5 )0

(g) (13 )5

(j) [2 3 2 × ( )3]2 (33 4 )3× ( 6 4)2 (4 3 2)2× (2 3)3

(k) (3 2 )7 (l) (2 3)2×4 2

(m) (52ℎ 32)4 (n) (3 ℎ 28)4 (o) (−( 22 ) 79)4
(p) (3234)3 (q) (7334)2 (r) (5325)2

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MODUL MATEMATIK PT3 TINGKATAN 3
(b) 2−11 ÷ 2−9
5.5 : INDEKS NEGATIF (e) ( 3)−5 × 12 ÷ −5
CONTOH 6

(a) (11−2)−4

(a) 3−5 × 3−3 = 3−5+(−3)
= 3−8
1
= 38

(b) 9 ÷ = 9−1
= 8

(c) ( −1)−7 (d) 3−6 × 38 × 3−4

(f) 24 × 4−3 ÷ 16−2 (5−1×2−4)−3 ( −5 −1)−2

(g) (52)4×2−9 (h) ( 2 −4)3

(i) (6 −4)3 ÷ ( 4)−2 5 −8( 2 3)−3 (k) 8( 2 −1)3 × (1 2 ÷ ( 2 )−3

(j) ( 5 4)−2 2 −3 3)

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MODUL MATEMATIK PT3 TINGKATAN 3
(c) ( 2)−4 × 8 ÷ −6
LATIHAN 6

A. Permudahkan setiap yang berikut.
Simplify the following.

(a) ( 5)−4 (b) 6−8 × 62 × 6−4

(d) (6−6)−2 (e) (8−2)−7 3 −5 ( 3 4 )−2

(f) ( 5 2)−2

( −3 −3)−2 (h) (4 −2)3 ÷ (2 5)−5 (i) ( 3 −2)2 × ( −2 2)4 ÷ ( 5 )−3

(g) ( −7)2

(7−5×3−4)−2 (k) 16(ℎ2 −1)5 × (1 ℎ−3 3)4 (l) ( 5 2)3 ÷ ( 3 )−3
4
(j) (74)3×3−5

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MODUL MATEMATIK PT3 TINGKATAN 3

5.6 : INDEKS PECAHAN 2
CONTOH 7
(b) 83
3
( 3 ÷ 2 × 1 × 32
(a) 92
34)3 ( 2 2)
4
( 3×23 ÷ 43×23) × ( 21+23 2
(d) 325
)

=( 2 ÷ 1 × 4

2)

= 2−21+4 11

= 2

3 1 43
7
(c) 162 (e) (34 × 32)3 × ÷ 3)4
(33

19 2 3 2 52 56
(f) (75)5 × (72 ÷ 75)
(23×213)5 (h) ( 3 × 3) ÷ ( 6)

(g) 3 1 4

(24÷24)

31 3 24
5 521)3 1
814×92 162 (k) × ÷ × 5)5
(52 (54
(i) 2 (j) 2

273 4×643

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MODUL MATEMATIK PT3 TINGKATAN 3

LATIHAN 7 3

A. Permudahkan dan cari nilai setiap yang berikut. (c) 164
Simplify and find the value of each of the following.

3 2

(a) 92 (b) 643

4 32 7 56

(d) 1255 (e) 164 × 273 (f) (56 ÷ 56)

2 × 53 ÷ 2 × 3 1 12 (i) (4 × 2)2 × (8−2)2

(g) (33 33) (33 33)11 (h) (33)3 ÷ (32 ÷ 32)

(j) (32)3 ÷ (3 × 2−3)2 4 3

( 3 9)3 ( 2 6)2

(k) 4 (l) ( 3×4 6)2

( 5)5×( 2 )2

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MODUL MATEMATIK PT3 TINGKATAN 3

5.7 : HUKUM INDEKS
CONTOH 8

2 22 1 163
(b) (5 2 5) × 5−1 −3 5
(a) 8−3 × 83 × 29 (a) 1
41
2 43×42
=52 4 5 × 5−1 −3 5
=(23)−3 × (23)3 × 29 =52−1 4−3 54+51 35

=2−9 × 22 × 29 =5pq 92×92
=2−9+2+9
=22 (d) 33
=4

(b) ( −21 3 × 7 7

) 2 (c) 273 × 3−9 × 92

11 1 −4 32

52×4×52 (f) (3−4 × 2−3)2 ÷ (24 × 32) (g) (4 × 7−3)3 ÷ (49−2 × 22)

(e) 42

12 1 34 31 1 1 1 13

(2×42×9−2) (i) (28 2) × (10 )2 ÷ (5 )2 (j) (9 3 3 )2 ÷ ( 2 6)

(h) 1 1 4

(24×273)

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MODUL MATEMATIK PT3 TINGKATAN 3

LATIHAN 8 1 32

A. Permudahkan dan cari nilai setiap yang berikut. 33×(42×22)
Simplify and find the value of each of the following.
(c) 27
11 4
3 321)5 3
62×242 (b) ÷ ×
(814 92
(a) 3

164

7 32 (e) (8 )2 × (2 )−2 × 2 10−3×10002

[ 2×( )2 ] 83 (f) 1 9

(d) 3 (103) ×10−2

3−2×27 1 12

(g) 1 2 (h) ( −2)3 × 7 ÷ 4 (i) ( 2) ÷ −3 × 5

(2×643)

53 36 13

4× 4 ( 4 −2)3×( 2) 273×92

(j) −2 (k) 6 (l) 3

814

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MODUL MATEMATIK PT3 TINGKATAN 3
(b) (−2 2 )3 × ( 3)2 ÷ 4 7
CONTOH 8 : SOALAN KBAT

Selesaikan setiap yang berikut.
Solve each of the following.

(a) (3 2 )4 ÷ 8 7 × ( 3)2

(c) (5 2)3 × ( 3)2 ÷ 3 8 13

(d) (9 2 )2 × ( )2 ÷ −1

15 4 (f) √36 2ℎ3 × 6 2 3

(4 3) × 3 1

(e) 16 2 (4 ℎ)2

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MODUL MATEMATIK PT3 TINGKATAN 3

LATIHAN 8 : SOALAN KBAT

Selesaikan setiap yang berikut.
Solve each of the following.

22 1 1 1 1 13
(a) (3 2 5) × 3−1 −3 5
(b) (4 3 3 )2 ÷ ( 2 6)

(c) (3 −4)3 ÷ ( 3)−2 (d) ( 3 −4)2 × 4 3 ÷ ( 3 −2)3

(e) (9 3 −1)3 × (1 −2 3)2 ÷ (4 2)3 (f) (3 4)2 × ( 3)2 ÷ 3 10

3

18