# Simplify a power of a power

## Home learning focus

Learn how to simplify a power of a power.

This lesson includes:

- one video
- a learning summary
- two activities with answers

*Created in partnership with Beyond.*

# Learn

## Indices

Squares, cubes and higher powers are shown as small digits called **indices** (the singular form is **index**), also commonly known as **powers** or **exponents**. Indices are used to show numbers that have been multiplied by themselves, and can also be used instead of the **roots**, such as the square root.

The mathematical laws around indices make complex calculations involving them easier.

### Simplifying a power of a power

You may be asked to **simplify a power of a power** or **raise indices to a power**, eg Simplify (aᵐ)ⁿ

If this happens, you are being asked to multiply everything **inside** the bracket, by itself, the number of times **outside** the bracket. When raising one power of a number to another, you simply **multiply the powers together**.

(aᵐ)ⁿ = aᵐ ˣ ⁿ

Follow the slideshow below to learn more about **simplifying a power of a power**, which is one of the index laws. Read through each example, following the steps closely to see how each solution is arrived at.

For a short further explanation to aid your understanding of raising indices to a power before simplifying, watch the section between **2:44** and **3:11** in this video from BBC Bitesize, National 5 Maths.

# Practise

## Activity 1

**Simplifying a power of a power - mixed practice**

Now test your understanding and knowledge of raising a power to a power by working through these worksheets from Beyond. Questions are grouped by difficulty either as Bronze, Silver or Gold so aim to get as far as you can! There is also a challenge to complete at the end. Write your answers on a piece of paper.

Click here for the answer sheet.

## Activity 2

**Indices - skills**

Keep going: test your understanding of the laws of indices with this worksheet from Beyond that covers multiplication, division and raising indices to a power. If you need to strengthen your knowledge of the laws of indices first, check out the other BBC Bitesize Daily, Year 9 and S3 Maths lessons from this week.

Click here for the answer sheet.

# There's more to learn

Have a look at these other resources around the BBC and the web.