Students keep making the same mistakes in their GCSE Maths exams. Inspired by the examiner's reports find out where students are losing vital marks, so that you can avoid the common slip-ups!

# 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:**

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*## GCSE Maths Banana skins - Don't slip up!