When we raise numbers to powers, there are lots of interesting properties to be discovered. We hope this selection of problems will pique your interest and help you to develop your understanding of powers and indices.

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Power mad!
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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Power countdown
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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Tens
When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?


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Indices and surds

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Powers and roots: Age 11-16
Working on these problems will help you develop a better understanding of powers and roots.