Before You Watch

This video deals with numbers called indices, specifically as applied to algebra. We often call them powers, or exponents. An example is the number 35, which we read as “three to the power of five”. This means three times itself five times:

35 = 3 x 3 x 3 x 3 x 3

Here the number 5 is called the exponent or the index. The plural of index is indices.

This definition of indices, or exponents, is well demonstrated here:

This topic builds on the fundamental concepts of algebra covered in Introduction to Algebra. If you need a refresher on algebra in general, watch that video first, then come back.

The Video

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Some Practice Questions


Now What?

Comfortable with the concepts covered in this video? A great next step would be to look at Negative and Fractional Indices  for a more complete picture of the rules surrounding indices.

But When I am Going to Use This

Indices are used in many different situations in real life. A common example is in writing very large or very small numbers. These are often written in scientific notation, and can be stored in computers as a type of variable known as a floating point variable. Scientific notation makes heavy use of indices to keep numbers easier to work with. Floating point variables are very important in all areas of computing, including gaming physics.

Indices are also used in the calculation of areas and volumes. For example, the area of a square is the length squared, and the volume of a cube is the length cubed. This is especially important when changing units of measurement, such as from cubic metres to cubic centimetres.

Plus, indices are used in certain kinds of other measurements, including acidity (pH), the loudness of sound (decibels), or the intensity of earthquakes (the Richter scale). All of these measurements use what is known as a logarithmic scale, which relies on indices.

Other Links

Maths Is Fun has a useful applet to help you understand the basic idea of indices, followed by an easy to follow summary of the rules.

Another page with a lot of interactive maths problems is It is well structured at the top level and things are easy to find.

Laerd Mathematics gives a succinct summary of the rules, and follows this up with a wide selection of questions. Worked answers are available.

The Khan Academy has a comprehensive set of video tutorials covering a large range of mathematical and other concepts, as well as questions to test your knowledge. This link takes you to the relevant section for this topic.

Patrick JMT (Just Maths Tutorials) has many video tutorials covering a large range of mathematical concepts. Here are two useful videos: the first one covers the basic indices rules, and the second provides example questions.