# Indices

## Indices

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.**

*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 is a **root.**

**Rule 6**

Anything to a power of 1 is just itself and we normally don't bother putting the 1 there i.e. 5^{1} is just 5.

Anything to a power of 0 is equal to 1, it doesn't matter what number it is!

i.e. 10^{0} = 1, 2^{0} = 1, x^{0} = 1, etc.

There you go! There's your rules. Now practice using them by doing some questions!

**Drag and drop the appropriate rule onto the formula you would use it to solve:**

The rules of Indices also work in Algebra (after all the letters or **variables** represent numbers anyway!).

So with algebraic fractions you can take the powers at the bottom from the powers at the top and simplify the expression (a bit like **cancelling **the powers on the top and bottom of the fraction).

What are we talking about? Good question! So here's an example.

**Click the Play and Next buttons to see how it is done:**

*
*