# Indices/Exponents

### Introduction to Indices

### Video

This video from *Khan Academy* introduces the concept of indices/exponents as repeated multiplication and discusses a few examples.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

### Notes

These notes from MathCentre explain the concept of indices and give some examples. There are exercises with answers for you to use for practice.

A pdf of this document can be downloaded here.

### Interactive Exercises

This NUMBAS exercise asks you to evaluate various numerical expressions involving indices.

Please click here to view this NUMBAS question in another window.

### Negative and Fractional Indices

### Video

This video from *Khan Academy* gives a nice intuition for why a negative power corresponds to taking a reciprocal. It goes through examples of this for positive and negative integers, along with an example of a fraction to a negative power.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

### Notes

These notes from MathCentre show how to work with negative and fractional indices, by giving the relevant rules and some worked examples. There are also tips on using your calculator for these types of problems. There are exercises with answers for you to use for practice.

A pdf of this document can be downloaded here.

### Interactive Exercises

This NUMBAS exercise lets you practise working with fractional and negative indices.

Please click here to view this NUMBAS question in another window.

### The Laws of Indices/Exponents

### Videos

This video from *Khan Academy* shows where the rules for multiplication and division of like terms involving indices come from, and gives some worked examples.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

This video from *Maynooth University* gives a nice description of how to raise more complicated expressions to a power, as well the reasoning behind the rule.

Note: All *Maynooth University* content is available for free at msc.maths.nuim.ie.

This video from *Maynooth University* gives a nice explanation of the rules of taking powers of expressions involving indices.

Note: All *Maynooth University* content is available for free at msc.maths.nuim.ie.

### Notes

These notes from MathCentre give a nice brief overview of the rules of indices, along with some examples. There are exercises with answers included for you to practise with.

A pdf of this document can be downloaded here.

### Interactive Exercises

This NUMBAS exercise asks you to simplify expressions using the laws of indices.

Please click here to view this NUMBAS question in another window.