# Maths:Indices and Standard Form

- Created by: Wunmi
- Created on: 29-10-10 14:44

### Indices

#### Powers and Roots

A ** power **tells you to multiply a number

**by itself**.

For example, 5^{3} means 5 x 5 x 5 which is 125.

2^{4} means 2 x 2 x 2 x 2 which is 16.

**It is a short way of writing out calculations.**

For example, 3^{3} x 4^{2} = 3 x 3 x 3 x 4 x 4 = 432

A **root **is the opposite of a power.

For example:

- means 'what number do you square to get 4?'* *

**The answer is 2.**

- means 'what number do you cube (multiply by itself 3 times) to get 27?'

**The answer is 3.**

*Rules of indices*

*There are several rules that you will need to know.*

**Rule 1**

*When you multiply indices of the same number you add the powers.*

**For example: ****5 ^{4} x 5^{3} = 5^{4 + 3} = 5^{7}**

**Rule 2**

*When you divide indices of the same number you subtract the powers.*

**Rule 3**

Indices outside a bracket **multiply.**

**For example:****(3 ^{2}) ^{4} = 3^{2 x 4} = 3^{8}**

**Rule 4**

**Negative indices** mean **reciprocal**, i.e. 'one over...' or 'put on the bottom of a fraction'.

**Rule 5**

When the power is a **fraction **the top of the fraction (numerator) is a **power **and the bottom of the fraction…

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