Indices

CHAPTER 8.

Indices

               Consider 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Here , the multiplication of the number 2 by itself is shown by writing it nine times. 

This multiplication is written as 2⁹. The number ‘2⁹’ is as exponential number .

           2⁹  is read as ‘ 2 raised to power 9’ or ‘2 to the power 9’ or ‘2 raised to 9’.

            

In the number 2⁹ , 2 is called the based of the number and 9 is called the index or exponent.

	Multiplication form	Index form	Base	Index
1.	7 × 7 × 7	73	7	3
2.	3 × 3 × 3 × 3 × 3	35	3	5
3.	9 × 9	92	9	2
4.	2 × 2 × 2 × 2 × 2 × 2	26	2	6
5.	1 × 1 × 1 × 1 × 1	15	1	5

Example : study the following table :  

2³  = 2 × 2 × 2

2² = 2 × 2

2¹ = 2

2³ is read as the third power of two or the cube of two.

2² is read as the second power of two or the square of two.

2 ¹ = 2, i.e. the first power of a number is equal to the number itself. Therefore, if the index of a number is 1, it is the custom not write it.

       

 For example, 5 is the same as 5¹, 10 means 10¹, etc.