Page 101 - Mathematics_Form_Two

´´´´
kkkkk
k
k 5 8 = kkkkkkkk
´´´´´´´
1
= Exponents and radicals
kkk
´´
1 (c) æ 1 1ö 1
= (c) ç = = = 19 2
k 3 è 19 ø - 2 ÷ æ 1 ö 2 1
ç ÷ 19 2
k 5 è 19 ø
0
Thus, = k − 3 , for k ≠ .
k 8
FOR ONLINE READING ONLY
1 Example 5�13
Therefore, k − 3 = .
k 3 Express the following powers by using
1 1 negative exponents;
n
x
In general, 0, x ¹ - n = x n and x = x − n , 3
1
1 (a)  (b) (0.75) 16 Mathematics for Secondary Schools

for x 0, x ¹ . - n = 
4
x n 1
When n 1, x= - n = x - 1 = 1 = 1 . (c) 2
x 1 x 17
1 1
0,
If x ¹ then 0,x ¹ is called the reciprocal Solution

x
x
–1
of x, which can also be written as x .  3 3
1
1
4
(a)  = ( ) = 4 − 3
−
4

Example 5�12 (b) (0.75) = 1
16
Express the following exponential (0.75) − 16
numbers using positive exponents: (c) 1 2 = 17 − 2
(a) 4 –3 (b) a –7 17
1
(c)
19 - 2 Example 5�14
Solution Simply each of the following
3
1
-
(a) (a) 4 = ( ) 3 expressions by writing your answers in
-
4
positive exponents:
4 17
1 æö 3 x 5 ab
= ç÷ (a) (b)
10 11
4 èø x 7 a b
1 .
= Solution
4 3 5
x5
-
(a) x 7 = x 57
=
x57
-
(a)
x
7
7
(b) (b) a (b) a æ 1 - 7 - 7 = = a ( ) ö æ x7 - 2
-
1

( ) a
-
1
1 1
1ö 1
1
(c) 19 2 ç = 2 ÷ = = 2 ÷ = ç = x 2
= =
2
19 (c)
=
x
-
2
= 1 1 ö 1 ö
è 19 ø 1 - = = 1 æ 7 æ 2 - 1 19 ø è 1
1
7 ÷ ç
(b) 2 19 a - 7 = a( ) 7 19 2 = x2 2
-
a
1
=
7 ç ÷ 1
a 19 ø 19 ø
è
è
x
1 x5 5 1
= = Therefore, x = 1
a 7 Therefore, x x 7 x7 x 2 = 2 .
95
Student's Book Form Two
11/10/2024 20:12:18
MATHEMATIC F2 v5.indd 95
MATHEMATIC F2 v5.indd 95 11/10/2024 20:12:18