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