Powers

\({9}\) is a square number.

\(3 \times 3 = 9\)

\(3 \times 3\) can also be written as \(3^2\). This is pronounced "\({3}\) squared".

\({8}\) is a cube number.

\(2 \times 2 \times 2 = 8\)

\(2 \times 2 \times 2\) can also be written as \(2^3\), which is pronounced "\({2}\) cubed".

The notation \(3^2\) and \(2^3\) is known as index form. The small digit is called the index number or power.

You have already seen that \(3^2 = 3 \times 3 = 9\) and that \(2^3 = 2 \times 2 \times 2 = 8\).

Similarly, \(5^4\) (five to the power of \({4}\)) \(= 5 \times 5 \times 5 \times 5 = 625\)

and \(3^5\) (three to the power of \({5}\)) \(= 3 \times 3 \times 3 \times 3 \times 3 = 243\).

The index number tells you how many times the number should be multiplied.

When the index number is two, the number has been squared.
When the index number is three, the number has been cubed.
When the index number is greater than three you say that it has been multiplied to the power of.

For example:

\(7^2\) is 'seven squared'.

\(3^3\) is 'three cubed'.

\(3^7\) is 'three to the power of seven'.

\(4^5\) is 'four to the power of five'.

Question

Look at the table and work out the answers. The first has been done for you.