You can evaluate powers yourself or with a calculator by multiplying the number by itself the number of times shown by the power or index. Finding the root is often easiest using the root button on a calculator.

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.