Page 95 - Mathematics_Form_Two

Exponents and radicals

8. Simplify, then use a calculator to Therefore,
check the answer: 5 2 5 ´ 3 ( = 5 5 ´ ) ( ´ 5 5 ´ 5 ) ´
(a) ( ) 1− 13 = !"# !$"$#

5 5555´ ´´´
(b) ( ) 1− 5 !""#""$

(c) ( ) 1− 2 Count how many times 5 is multiplied
FOR ONLINE READING ONLY
(d) ( ) 2−− 6 by itself. The answer is five times, which
gives the exponent. Thus, 5 is multiplied
(e) ( ) 2− 6 by itself five times. The exponent 5 can

( ) 5
(f) −− 4 also be obtained by adding the exponents Mathematics for Secondary Schools
(g) ( ) 5− 4 from each base. That is,
2+3
= 5 .
5
3
5 × 5 = 5
2
9. Write each of the following in Similarly, if a is any number, then
power form whose base ia a prime
4
2
number choice: a × a = (a × a × a × a) × (a × a)
(a) 22× b = a 4+2
(b) 27 a = a 6 4 2 6
(c) 2 h Therefore, a × a = a
4
2 m Generally, if x is any non-zero number
(d) with positive exponents m and n, then
2 − m x m x ´ n x = m n + . This is called the
(e) 82× b multiplication law of exponents.

(f) 5 125× k

(g)   1   3 Example 5�6
 243  Simplify each of the following by using
multiplication law of exponents:
Laws of exponents (a) 7 × 7
6
8
There are three groups of exponents namely (b) 6 × 6 × 6 4
3
4
positive, negative, and zero exponents. 5 3 5 4
×
Simplification of the exponents are usually (c) ( ) ( )
9
9
based on the four laws called multiplication, (d) (0.45) × (0.45) × (0.45)
4
2
12
division, power, and zero power.
Solution
Multiplication law for exponents
Consider the product of two exponential By using multiplication law of
exponents, it implies that,
numbers having the same base with 6 8 6+8 14
3
2
positive exponents such as 5 × 5 . The (a) 7 × 7 = 7 = 7
3
4
4
exponential numbers can be written in (b) 6 × 6 × 6 = 6 4+3+4 = 6 11
expanded form as follows: (c) ( ) ( ) ( ) = ( )
5 4
5 3
5 7
5 3+4
=
×
2
5 = 5 × 5 and 5 = 5 × 5 × 5 9 9 9 9
3
89
Student's Book Form Two
11/10/2024 20:12:13
MATHEMATIC F2 v5.indd 89
MATHEMATIC F2 v5.indd 89 11/10/2024 20:12:13