Page 106 - Mathematics_Form_Two

Exponents and radicals

1 1 1
⇒ 5 = 3 3 5   8   3 =   2 2 2   3
× ×
 4  1 4 1 4 × 4  27   3 3 3  1
 5  = 5 1 æ 3 ö 3
2ö
  æ 8 3 = ç æö ÷ = 2
= 5 ç 27 ø ÷ ç ç÷ ÷ 3
3
èø
è
è
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1 4 5 4 1 5 Therefore, æ ç 8 ø ÷ 1 3 = 2 ö .
Mathematics for Secondary Schools 5 5    5 = 1 5 = 5 5 5 × 5 5 Example 5�24 27 ø 3 1 3 ) �
⇒
5 =

1
è


=
5
⇒
Find the value of ( 125-
Based on the previous results, it can be
Express –125 as a product of prime
concluded that if x is a positive number Solution
and n is any positive real number, then factors.
–125 = (–5) × (–5) × (–5)
 n  1 n 1 1 n n ( 125- ) ( ( ) ) 1 3 = ( ) 5- 3 ´ 1 3 = - = - 5
1
3
5
 x  = x = x and x = . x 3
  1 1 1
3
5
( 125- ) ( ( ) ) 3 = ( ) 5- 3 ´ 3 = - = - 5
3
1
1
1 ) ( ( ) ) 1 3 ´
3
3 = -
( ) 5-
=
3
Generally, x = n , x for x > 0. ( 125- 3 5 = - 5
n
1
Therefore, ( 125- ) = - 5.
3
Example 5�22
1 Exercise 5�6
Find the value of 49 .
2
Solution Simplify each of the following
Express 49 as a product of prime factors. exponential numbers:
1
49 7 7 7= ´ = 2 1. (64)
2
1 1 2´ 1 1
3
2
Thus, 49 = ( ) = 7 2 = 7 1 2. (1000)
7
2
2
1 1
Therefore, 49 = 7. æ 81 ö 2
2
3. ç ÷
Example 5�23 è 625 ø
1
2
1 4. (0.25)
æ 8 ö 3
Simplify ç ÷ �
è 27 ø 1 3
Solution 5. (0.027)
Express the base in power form and 1
4
simplify. 6. (81)
100
Student's Book Form Two
11/10/2024 20:12:24
MATHEMATIC F2 v5.indd 100 11/10/2024 20:12:24
MATHEMATIC F2 v5.indd 100