Page 99 - Mathematics_Form_Two

Exponents and radicals

Example 5�10 x n æ x ö n

Generally, n = ç ÷ , where x, y and
Simplify each of the following y è y ø
expressions: n are real numbers and y ≠ 0. This is a
power of a quotient.
3 20
(a)
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3 12 Example 5�11
a 28 Write each of the following expressions
n
(b) in the form of æ x ö . :
a 17 ç ÷
è y ø Mathematics for Secondary Schools
13 2 æ 13 ö 2
(0.47) 10 (a) = ç ÷
(c) (0.47) 6 9 2 è 9 ø

Solution (b) (0.5) 4 4
(0.3)
(a) 3 20 = 3 20 12
-
3 12 (c) 16
= 3 8 3 2

a 28 Solution
-
(b) = a 28 17
a 17 13 2 æ 13 ö 2
= a 11 (a) 9 2 = ç è 9 ÷ ø

(c) (0.47) 10 = (0.47) 10 - 6 (0.5) 4 æ 0.5 ö 4
(0.47) 6 (b) (0.3) 4 = ç è 0.3 ø ÷
= (0.47 ) 4 2
4
(c) 16 = 4 2 = æö
ç÷
3
3 2 3 2 èø
When exponential numbers of different
bases with the same exponents are Exercise 5�3
divided, the number can be expressed as Simplify each of the following
a single exponent. If a and b are any real expressions:
numbers such that b ≠ 0, then: x 5
1.
2
´´´
a 4 = aaaa x
´´´
b 4 bbbb 2 7000
aaaa 2.
= ´´´ 2 6998
bbbb 625
4
= æ a ö 4 3. 5
ç ÷
è b ø
4. 6 4 (2 a 2 4a ÷ a + 2 )

93
Student's Book Form Two

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MATHEMATIC F2 v5.indd 93 11/10/2024 20:12:16
MATHEMATIC F2 v5.indd 93