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.

An index law tells you how to calculate an operation involving exponents, also known as an index, power or order, which is a small number placed to the upper-right of a base number. The exponent shows how many copies of the base number are multiplied together. In 6^3, 6 is the base number and 3 is the exponent and it can be written as 6 x 6 x 6. You should know the following index law: when raising one power of a number to another, you multiply them.

Index law: Raising one power of a number to another

To raise one power of a number to another, simply multiply them.

1 of 2

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.

Multiplying powers with the same base

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.

Simplifying a power of a power

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.

Laws of indices

Click here for the answer sheet.

There's more to learn

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

More lessons for Year 9 and S3
KS3 Maths
11-14 Maths
Play Nightfall
game
KS3 Computing on BBC Bitesize
Bitesize Support
Doubly Powerful