Squares, cubes and higher powers are shown as small digits called indices. The opposite of squaring and cubing are called square root and cube root. There are more rules we can use with indices.

Part of

\({9}\) 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.