# 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.

##### Stage: 3 and 4 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

##### Stage: 4 Challenge Level:

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

### Tens

##### Stage: 5 Challenge Level:

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

### Giants

##### Stage: 5 Challenge Level:

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?