Indices and Powers
An index or power shows how many times a number is multiplied by itself.
▶ Interact
Play with the controls to see the idea in action.
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An index or power shows how many times a number is multiplied by itself.
- 2 to the power 3 equals 8
- a to the m times a to the n is a to the m+n
- Any number to the power 0 equals 1
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Indices and Powers?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Indices and Powers. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Indices and Powers in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Indices and Powers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Indices and Powers in detail
An index, or power, shows how many times a number is multiplied by itself: 2⁵ means 2 × 2 × 2 × 2 × 2 = 32. The number being multiplied is the base and the small raised number is the index or exponent. Squares and cubes are the most common special cases.
Powers give a compact way to write repeated multiplication and very large or small numbers. Any number to the power 1 is itself, and any non-zero number to the power 0 is 1. They are used in area and volume, compound interest and scientific notation, and lead on to the laws of indices.
How the interactive helps you understand Indices and Powers
Watch the growth curve in the interactive. Use any sliders or buttons it offers to change the values and see how the growth curve responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Indices and Powers.
Real-life uses and examples
- Explain Indices and Powers to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Indices and Powers in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Indices and Powers by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Indices and Powers without checking why they work.
- Forgetting units, signs or brackets when you apply Indices and Powers.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Indices and Powers
What is Indices and Powers?
An index or power shows how many times a number is multiplied by itself.
What are the most important points about Indices and Powers?
The main points are: 2 to the power 3 equals 8; a to the m times a to the n is a to the m+n; Any number to the power 0 equals 1.
Why is Indices and Powers useful?
Understanding Indices and Powers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Indices and Powers?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Indices and Powers?
Related topics in Mathematics include Square Roots and Cube Roots, Rational and Irrational Numbers, Sets and Venn Diagrams.