Number
Powers and exponents
Read and write a power, work out its value, and use the laws for multiplying and dividing powers of the same base.
Writing 2 × 2 × 2 × 2 × 2 × 2 × 2 gets tiring, and it is easy to lose count. A power is shorthand for it: 2⁷ means seven twos multiplied together. The big number at the bottom is the base — the number being multiplied. The small raised number is the exponent — how many of them there are.
Watch out
2³ is not 2 × 3. It is 2 × 2 × 2, which is 8, not 6. The exponent counts the numbers; it is not one of them.
Have a play
This line runs to thirty-two in twos. Find 2, 4, 8, 16 and 32 on it, and see how far apart they get.
Tap anywhere on the line.
Worked example
What is 2⁴?
The base is 2 and the exponent is 4, so write out four twos: 2 × 2 × 2 × 2.
Reading the power back into a multiplication is the safest way to start, until the common ones are familiar.
Try it together
Now let us work out 2³ × 2² together — twice, two different ways.
Doing it the long way and the short way and getting the same answer is what makes the short way worth trusting.
1.The long way first. What is 2³?
Have a go
Have a go on your own: what is 4³?
Hint: Three fours multiplied together.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.