# 1.1 Indices

4.1 Indices

1.1.1 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

1.1.2 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

1.1.3 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

1.1.4 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

1.1.5 Negative Indices

${a}^{-n}=\frac{1}{{a}^{n}}$

Example:
${5}^{-2}=\frac{1}{{5}^{2}}=\frac{1}{25}$

1.1.6 Fractional Indices

Example: