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INTRODUCTION TO INDICES
In Secondary One, we learnt the square, the cube, the square root and the cube root of a number. For the square in Fig. 1.1, we know that its area is 2 × 2 = 4 unit . We have learnt that 2 × 2 can be written as 2 , and we read it as the square of 2’.
For the cube in Fig. 1.2, we know that its volume is 2 × 2 × 2 = 8 unit . We have also learnt that 2 × 2 × 2 can be written as 2 , and we read it as the cube of 2’.
In a similar way, the expression 2 × 2 × 2 × 2 × 2 × 2 can be denoted by 2 . In the notation 2 , the number 2’ is known as the base and the digit 6’ is known as the index or exponent . We read 2 as 2 to the power 6 or 2 to the 6 power.
In general, we have the following
If a is a real number and n is a positive integer, we have
n times
a = a × a ×
× a .
where a is called the base and n is called the index or exponent.
When n = 1, we have a = a.
The index notation, a , is read as a to the power n , or a to the nth power, or the nth power of a .
Example
1
Calculate:
(a) 1.8
3
(b)
(c) (3)
4
(d) (1)
5
Solution
(a) 1.8 = 1.8 × 1.8 × 1.8 = 5.832
3
(b)
(c) (3) = (3) × (3) × (3) × (3) = 9 × (3) × (3) = 27 × (3) = 81
4
(d) (1) = (1) × (1) × (1) × (1) × (1) = 1
5
2
2
3
3
6
6
6
th
n
1
n
Fig. 1.1
Fig. 1.2
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