## Indices |

We know that: 5 × 5 = 25The product 5 × 5 can be written as 5 ^{2}.
5 × 5 is known as the Generally when a number is multiplied by itself any number of times, the expression is simplified by using the index notation. ## Note:- 2 is called the
**base**. - 3 is called the
**index**or**power**(or**exponent**) because it indicates the power to which the base, 2, is raised. - 8 is the
**basic numeral**(or**number**). - 2
^{3}is read as ‘2 to the power 3’ or simply ‘2 cubed’.
## That is:## Example 1Write 4 ## Solution:## Note the following:- 64 = 4
^{3} - 3 is the power (or index or exponent)
- 4 is the base number
- 64 is a basic numeral or number
- 4
^{3}is the index form (or power form) of 64 - 4 × 4 × 4 is the expanded form of 64
- For 64 = 4 × 4 × 4 = 4
^{3}, the base number 4 appears three times as a factor of the basic numeral (or number) 64 - 4
^{3}is read as ‘4 to the power 3’ or simply ‘4 cubed’
## Example 2Write each of the following expanded forms in index form: ## Solution:## Example 3Write each of the following in expanded form: ## Solution:## Example 4Find the value of the following: ## Solution:## Example 5Write 16 in index form using base 2. ## Solution:## Example 6Write the following numbers as a product of prime factors: ## Solution: |

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