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How Powers Behave
How Powers Behave
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.
Power Mad!
Age 11 to 14
Challenge Level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Power Countdown
Age 14 to 16
Challenge Level
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.
Tens
Age 16 to 18
Challenge Level
When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?
Giants
Age 16 to 18
Challenge Level
Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
Related
Powers and Roots
Indices and Surds