# Indices (2023)

Year 8 Interactive Maths - Second Edition

## Indices

We know that:
5 × 5 = 25

The product 5 × 5 can be written as 52.

(Video) Negative and Fractional Indices (Higher Only) | GCSE Maths Tutor

5 × 5 is known as the expanded form (or factor form) of 25 and 52 is known as the index form of 25.

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).
• 23 is read as '2 to the power 3' or simply '2 cubed'.

#### Example 1

Write 43 as a number.

##### Solution:

###### Note the following:
• 64=43
• 3 is the power (or index or exponent)
• 4 is the base number
• 64 is a basic numeral or number
• 43 is the index form (or power form) of 64
• 4 × 4 × 4 is the expanded form of 64
• For 64=4 × 4 × 4 = 43, the base number 4 appears three times as a factor of the basic numeral (or number) 64
• 43 is read as '4 to the power 3' or simply '4 cubed'

#### Example 2

Write each of the following expanded forms in index form:

(Video) Laws of Indices - Part 1 | Algebra | Maths | FuseSchool

#### Example 3

Write each of the following in expanded form:

#### Example 4

Find the value of the following:

(Video) Math Antics - Intro To Exponents (aka Indices)

#### Example 5

Write 16 in index form using base 2.

#### Example 6

Write the following numbers as a product of prime factors:

##### Solution:

(Video) GCSE Maths - Introduction to Powers/Indices & 3 Basic Rules (Powers Part 1/6) #29

###### Key Terms

indices, expanded form, factor form, index form, base, index, power, exponent, basic numeral, basic number

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(Video) Laws of Indices - Part 1 (Higher & Foundation) | GCSE Maths Tutor

## Videos

1. The Maths Prof: The Rules of Indices / Exponents (part 1)
(The Maths Prof)
2. How to work with indices (powers).wmv
(maths520)
3. Indices: How to Solve Indices Problems||Rules of Indices
(Precious Ugwueze)
4. What are Indices & How to Trade Them?
5. Indices (घातांक)
6. Indices
(Maths Genie)
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