Page 96 - Mathematics_Form_Two

Exponents and radicals

(d) (0.45) × (0.45) × (0.45) = Furthermore, the expression (7 × 5) , can
4
12
3
2
(0.45) 2+4+12 = (0.45) 18 be written in expanded form as follows:

3

(7 × 5) = (7 × 5) × (7 × 5) × (7 × 5)
4 3

Suppose the expression (2 ) is to be = 7 × 5 × 7 × 5 × 7 × 5

written as a single exponent, then it can = 7 × 7 × 7 × 5 × 5 × 5

be written in expanded form as follows: Therefore, (7 × 5) = 7 × 5 .
= 7 × 5
3
3
FOR ONLINE READING ONLY
Mathematics for Secondary Schools Therefore, (2 ) = 2 4×3 = 2 . Similarly, if a and b are real numbers,
4 3
4
4
4
(2 ) = 2 × 2 × 2
3
3
3
4+4+4
= 2

4×3

= 2
then (a × b) can be expanded as follows:
4
12
= 2
4
(a × b) = (a × b) × (a × b) × (a × b) ×
12
4 3
(a × b)
2 4
Similarly, consider a number (a ) , where
a is any real number. The number can be
4
4
= a × b
written as a single exponent as follows: = (a × a × a × a) × (b × b × b × b)
4
4
4
2
(a ) = a × a × a × a 2 Therefore, (a × b) = a × b .
2
2 4
2
= a 2+2+2+2 Generally, (a × b) = a × b , where a
n
n
n
= a 2×4 and b are real numbers and n is a positive
= a 8 integer is known as the power law of a
8
2 4
Therefore, (a ) = a 2×4 = a . product.
mn
Generally, (x m n x , where m and n
) =
are positive integers and x is any real Example 5�8
number. This law is known as the power
law. Simplify each of the following by using
the power law of a product.
Example 5�7 (a) (7 ´ c 34
)
2
Simplify each of the following by using (b) (4 b ´ 2 c ´ 33 )
power law of exponents:
(a) (3 ) (c) (0.7 × 0.3 )
6 3
4
2 4
(( ) )
3 6 2
(b) 7 Solution
2
) =
(c) (0.7 ) (a) (7 ´ c 3 4 7 2 4´ ´ c 34´
7 3
8
= 7 ´ c 12
Solution 8 12
=
6 3
18
(a) (3 ) = 3 6×3 = 3 (b) (4 b ´ 2 c ´ 3 3 7 c 1 3´ b ´ 2 3´ c ´ 33´
4
) =
(( ) ) ( ) ( )
3 12
3 6 2
3 6×2
(b) 7 = 7 = 7 = 4 ´ 3 b 6 c ´ 9
3
69
= 4 b c
(c) (0.7 ) = (0.7) 7×3 = 0.7 21
7 3
90
Student's Book Form Two
11/10/2024 20:12:14
MATHEMATIC F2 v5.indd 90 11/10/2024 20:12:14
MATHEMATIC F2 v5.indd 90