Page 100 - Mathematics_Form_Two

Exponents and radicals

5 3
a b 7 3
5. Alternatively, 7 = 33 7 = 0 1 = . (2)
-
2
ab 7 3
 k mn  3 4 6 3 From equations (1) and (2), it follows that
6.  2 3 
km n
7 = 1
0
 7.   20a b  3  2  ×   5a b  3 25  5 Similarly, m 4 = mmmm´ ´ ´ = 1 (3)
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Mathematics for Secondary Schools 8. 8a b   15a b  Thus, m 4 4 = m m 44 = mmmm´ ´ ´ (4)
0, then
if m ¹
5ab

4
15a b c
3 2 2
0
m
-

m
3
5a bc
4 5
48a b
Therefore, m 0 = 1 by equations (3) and (4).
9.
2 3
1
3
10.
then x = 1. In this case 0 is not defined.
0
0
6r ÷ 4r Generally, if x any non-zero number,
(3 ´ 2 2 ´ 15 3 ´ 10 25 ) 3
11 2 Negative exponents
(3 16 2 ´ 16 5 ´ 2 ) 8 3
The expression 8 5 , can be simplified
(3mn ) 3 using the division law of exponents as
12.
( 8 mn ) 3 follows:
8 3 8 × 8 × 8
(3 ´ 2 a 3 b ´ 4 c ´ 2 ) 3 8 5 = 8 × 8 × 8 × 8 × 8
13. 2 1
(14 c ´ 2 a ´ 2 b ´ 3 ) = 8 × 8
( 17 ´ ( ) ) 3 = 1 2
2
4x
3
14. 8
( ( ) ´ 17 2 ) 3 Therefore, 8 3 = 1 . (1)
2
2x
8 5 8 2
15. (ab+ ) 2 Also, 8 3 8 = 35 - 8 = 2 - (2)
2
a − b 2 8 5
Zero exponent Comparing equations (1) and (2), gives
1
−
2
An expression 7 3 3 can be simplified by 8 = 8 2 . .
7
using the division law of exponents as k 5 kkkkk
´´´´
follows: Similarly, k 8 = kkkkkkkk
´´´´´´´

7 3 777´ ´
= = 1 (1) = 1
7 3 777´ ´ kkk
´´
1
94 =
k 3 Student's Book Form Two

11/10/2024 20:12:17
MATHEMATIC F2 v5.indd 94
MATHEMATIC F2 v5.indd 94 11/10/2024 20:12:17