Before You Watch

This video builds directly on the work done in the topic Indices Laws, and also introduces new laws. Make sure you are familiar with the following rules of indices before watching this video:

  • an x am = a(n+m)
  • an / am = a(n-m)
  • (an)m = a(n x m)

Confident in the use of these laws of indices? Then you're ready for this video! If not, watch Indices Laws first, then come back.

The Video

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Some Practice Questions

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Now What?

This video, along with Indices Laws, covers important concepts in algebra that you will continue to run into throughout mathematics, such as in calculus and more advanced areas. So it's very important that you're familiar with these rules and comfortable using them.

Once you are confident with these rules, why not check your skills in some of the areas covered by the other algebra videos? Look at, for instance, Factorisation of Algebraic Expressions  or Algebraic Fractions.

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 useful applets to help you understand the basic idea of indices, plus an easy to follow summary of the rules. The first link below is the same as for the topic Indices Laws and also covers negative indices and an index of zero. The next two links cover negative and fractional indices respectively. Sample questions are provided.

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

Patrick JMT (Just Maths Tutorials) has a comprehensive set of video tutorials covering a large range of mathematical concepts. Here are two relevant videos: the first runs through the use of negative indices, the second explains fractional exponents. On both of these pages are links below the video to more videos covering example questions.