5.1 Indices


5.1 Indices

5.1.1 Indices
1.   A number expressed in the form an is known as an index notation.
2.   an is read as ‘a to the power of n’ where a is the base and n is the index.
Example:

3.  
If a is a real number and is a positive integer, then




4.   The value of a real number in index notation can be found by repeated multiplication.
Example:
6= 6 × 6 × 6 × 6
= 1296


5.  
A number can be expressed in index notation by dividing the number repeatedly by the base.
Example:
243 = 3 × 3 × 3 × 3 × 3
= 35



5.1.2 Multiplication of Numbers in Index Notation
The multiplication of numbers or algebraic terms with the same base can be done by using the Law of Indices.
 
am  × an = am + n
 
Example:
33 × 38 = 33+8
= 311


5.1.3 Division of Numbers in Index Notation
1. The Law of indices for division is:
 
am  ÷ an = am - n
 
Example:
412 ÷ 412 = 412-12
= 40
= 1

2. a0 = 1


5.1.4 Raise Numbers and Algebraic Terms in Index Notation to a Power
To raise a number in index notation to a power, multiply the two indices while keeping the base unchanged.
 
(am ) n  = (an ) m  = amn
 
Example:
(43)7 = 43×7
= 421


5.1.5 Negative Indices

a n = 1 a n

Example:
5 2 = 1 5 2 = 1 25



5.1.6 Fractional Indices

a m n = a m n  or  ( a n ) m

Example:
64 2 3 = 64 2 3  or  ( 64 3 ) 2       =16


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