Myriora Maths › Maths foundations › Chapter 7: Order of operations and powers

Powers

Ages 9–11Chapter 7 · Lesson 3

In this lesson

A power means multiplying the same number again and again.
The small number says how many to multiply.
Squared is the power of two, and cubed is the power of three.
And powers grow very fast!

Your turn

Which is bigger: two to the power of five, or five to the power of two?

Show the answer

Two to the power of five is five twos multiplied: thirty-two. Five to the power of two is five times five: twenty-five. So two to the power of five is bigger, even though five is the bigger number!

The common mistake

Here's a question that catches lots of people. What is two to the power of three? Some people say six, because they do two times three. But the power means three twos, multiplied: two times two times two is eight!

Try it at home

Fold a sheet of paper in half again and again. Count the layers each time: 2, 4, 8, 16... how many after 5 folds?

Read the whole lesson

Hello, and welcome to Myriora Maths! Two times two times two times two times two. That's a lot to write! Powers are a short way to write it. Let's see how they work.

Times means adding the same number again and again. Three times four is four, plus four, plus four. A power means multiplying the same number again and again. Four to the power of three is four, times four, times four: sixty-four.

The big number is called the base. The small raised number is called the power. It tells you how many of the base to multiply together. So two to the power of five means five twos, multiplied: thirty-two.

You've already met two powers. Squared means to the power of two, like five squared is twenty-five. Cubed means to the power of three, like two cubed is eight. After that, we just say to the power of four, to the power of five, and so on.

Powers grow very fast. Start with one grain of rice, and double it every day. Two, four, eight, sixteen... After ten doublings, that's two to the power of ten: one thousand and twenty-four grains! Compare that with two times ten, which is only twenty.

Let's try one together. What is three to the power of four? Say it out loud!

That's four threes, multiplied. Three times three is nine, times three is twenty-seven, times three is eighty-one!

Your turn! Which is bigger: two to the power of five, or five to the power of two? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Two to the power of five is five twos multiplied: thirty-two. Five to the power of two is five times five: twenty-five. So two to the power of five is bigger, even though five is the bigger number!

Quick review. A power means multiplying the same number again and again. The small number says how many to multiply. Squared is the power of two, and cubed is the power of three. And powers grow very fast! See you next time!