Chapter 3: Powers, roots and indices
The chapter problem
Repeated doubling
A computer file starts at 1 unit. In each round, its size doubles. After 20 rounds, predict whether its size is nearer one thousand or one million units. You do not need an exact answer yet.
By the end of this chapter, you will use powers and index laws to find and estimate the size.
By the end of this chapter
You will be able to:
- calculate powers and roots, including square roots and cube roots;
- estimate powers and roots by comparing with nearby known values;
- use index laws to simplify products, quotients and powers;
- work with zero, negative and fractional indices.
Roadmap
- 3.1 Powers and roots
- 3.2 Estimating powers and roots
- 3.3 Laws of indices
- 3.4 Negative and fractional indices (Higher only)
- Review
Your turn to connect it
Where have you seen something grow by repeated multiplication, or where might a large number need estimating? Write one example from your life or someone else's.