Chapter 3: Review

Resolve the chapter problem

After 20 rounds, the file size is $2^{20}$. Split the power into two equal groups of ten factors:

The size is $1,048,576$ units. It is about $1,000,000$ units and far from $1,000$ units, so it is nearer one million. The estimate from 3.2 was reasonable.

Mixed practice

Work through the questions without notes first. For each one, choose the method and give a reason for your choice.

1. Work out $5^3$. Which operation does the index describe?
2. Estimate $\sqrt{130}$ to the nearest whole number. Give a reason using two squares.
3. Simplify $p^4p^6$. Which index law applies?
4. Simplify $(q^3)^2$. Explain why the indices multiply.
5. Write $8^{-2}$ as a fraction. Which earlier rule helps?
6. Work out $125^{2/3}$. Which root should you find first?
7. A rectangle has area $144\text{ cm}^2$. Work out its side length if it is a square.
8. A sequence starts at 3 and doubles five times. Write its final value as a power product and evaluate it.

Reflection

Write one example of a power or root you can now calculate. Then name one question you would check by estimating before calculating exactly.