Page 18 - SM inner class 8.cdr

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Chapter2 6 ½ –

Exponents

So we can say that for any rational
Introduction a
number ,
In the previous class, we have learnt that b
n n
a
exponents are a shortened way to show how æ a ö = ( )
è
b ø
many times a number is multiplied by itself. ç ÷ ( ) n
b
Let us recall.
Example 1. Express the following in power
Expressing the Numbers in Exponential notation:
Form with Integers as Exponent -2 -2 -2
(i) ´ ´
4
We can express 3 ´ 3 ´ 3 ´ 3 = 3 , where 3 is the 7 7 7
5 5 5 5 5 5 5
base and 4 is the index or power. (ii) ´ ´ ´ ´ ´ ´
3 3 3 3 3 3 3
n
In general, a is the product of ‘a’ with itself n 3
-2 -2 -2 æ 2
- ö
times, where ‘a’ is any real number and ‘n’ is Solution: (i) ´ ´ = ç ÷
any positive integer .‘a’ is called the base and 7 7 7 è 7 ø
‘n’ is called the index or power. 5 5 5 5 5 5 5 æ ö 7
5
(ii) ´ ´ ´ ´ ´ ´ = ç ÷
3 3 3 3 3 3 3 è ø
3
How to read Exponential Form?
Example 2. Express each of the following as
3
7 is read as 7 raised to the power 3 (or) 7 cube.
rational number:
Here 7 is called the base, 3 is known as 3 4
æ
2ö
- ö
exponent (or) power (or) index. (i) ç æ 5 ÷ (ii) ç ÷
è 7 ø è 3 ø
6
Similarly, 5 is read as 5 raised to the power 6.
Solution:
For example:
3
æ 5
- ö
- ö
- ö
(i) We can write -5 ´ -5 ´ -5 ´ -5 in the (i) ç - ö æ 5 ÷ ´ ç æ 5 ÷ ´ ç æ 5 ÷
÷ = ç
4
exponential form as (-5) and is read as è 7 ø è 7 ø è 7 ø è 7 ø
-5 raised to the power 4. Here, (-5) is the = -125
base and 4 is the power. 243
3 3 3 3 3 4
(ii) Also, ´ ´ ´ ´ in the exponential æ 2ö 2 2 2 2 16
2 2 2 2 2 (ii) ç ÷ = ´ ´ ´ =
è
5 3 ø 3 3 3 3 81
æ 3ö 3
form is written as ç ÷ and is read as 125
è 2 ø 2 Example 3. Express in the exponential
3 27
raised to the power 5. Here, is the base, form:
2
5 is the exponent. Solution: 125
This is called Exponential notation of 27
3
rational number. We can write 125 = 5 ´ 5 ´ 5 = 5
Similarly, and 27 = 3 ´ 3 ´ 3 = 3 3
5
3 3 125 5 3 æ ö 3
æ 2 æ 2 æ 2 æ 2 - ( 2 ) So, = = ç ÷
- ö
- ö
- ö
- ö
ç ÷ = ç ÷ ´ ç ÷ ´ ç ÷ = 27 3 3 è ø
3
è 5 ø è 5 ø è 5 ø è 5 ø - ( 5 ) 3
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Mathematics In Focus - 8