Page 97 - Mathematics_Form_Two

Exponents and radicals

4
2 4
(c) (0.7 × 0.3 ) (e) 3 23 4ab ´ ab
45
(0.7 × 0.3 ) )´
4
24
2 4
((0.7) 4 4 (0.3) 24 = (0.7) 44´ (0.7) 44´ ´ (0.3) 2 4´ (0.3) 2 4´ (f) æ 17 ö 2 ´ æ 17 ö 3 ´ æ 17 ö
´
(0.3) ) =
((0.7) ´
16
8
= (0.7) ´ (0.3) 8 ç è 20 ø ÷ ç è 20 ø ÷ ç è 20 ø ÷
16
= (0.7) ´ (0.3) .
4
2
(g) 16 × 16 × 16 4
3
3
æö 2 æö 3
FOR ONLINE READING ONLY
(h) ç÷ ´ ç÷
4
4
Example 5�9 èø èø
3
Write each of the following expressions (i) 10 × 10 0
by grouping together the letters with the (j) (0.58) × (0.58) × (0.58) 16
4
4
same exponents: 14 17 1 Mathematics for Secondary Schools
(a) d t (k) 3 × 3 × 3
4 4
r
p
4
5
(b) a × b (l) 10 × 10 × 10 10
5
2
(c) 3cd × 5c d 4 (m) 82 × 82 × 82 × 83
p
Solution (n) (0.1) × (0.1) × (0.1) 3
20
(a) d t = (dt 4 ) (o) b × b × b z
44
y
x
t
r
(b) a ´ b = ´ aa ´ 4 b 4 (p) k × k × k k
5
4
2
2
= ( a´ )ab 4 (q) x × x × x 2
p
t
= ( a )ab 4 (r) 10 × 10 × 10 s
2. Write each of the following
2
5c d = ´´´
4
d ´
(c) 3cd ´ 5c d = ´´´ 5 5 d ´ d 4 4 expressions in the simplest powers:
2
35 c c ´
5
d
2
3cd ´
5
35 c c ´
2
4
6
15 cd
´
=
´
2 4
= 15 cd . 6 6 (a) (4 ) (b) (a )
3 2
6
= 15(cd ) ) 6 6 (c) (b ) (d) (18 )
=
15(cd
4 3
1 20
3 2
2 5
(e) (71 ) (f) (a )
Exercise 5�2
6 1
(g) (19 ) (h) (23 )
2 n
1. Simplify each of the following
2 17
12 6
expressions and write the answers in (i) (m ) (j) (x )
power form: æ 3 ö 4 ö 4
(k) (2 ) (l) ç æ ÷
3 7
ç ÷
2
(a) 10 × 10 2 ç è è 4 ø ÷ ø
21 3
a b
1
(b) æö 3 ´ æ ç 1 ö ÷ 5 (m) (10 ) (n) (x )
ç÷
2
èø è 2 ø 3. Write each of the following
4
(c) r × r 8 expressions so that each base is
raised to a single exponent:
2
12
7
7
(d) æö ´ æö (a) (4 3)´ 2
ç÷
ç÷
6
6
èø èø
(b) (2 )a 2
91
Student's Book Form Two
11/10/2024 20:12:14
MATHEMATIC F2 v5.indd 91 11/10/2024 20:12:14
MATHEMATIC F2 v5.indd 91