# Arithmetic » What are powers?

## What is a power?

Powers are used to shorten calculations or formulas.

The calculation 7 × 7 × 7 × 7 × 7 can be shortened to 7^{5}.

You pronounce 7^{5} as 'seven to the power of five' or as 'seven to the fifth'.

## Base and exponent

In 7^{5}, 7 is called the *base* and 5 is called the *exponent*.

So: *base ^{exponent}*

## Special names

### Square

The ^{2} can be pronounced as *square(d)*.

Therefore 7^{2} can be pronounced as: 'seven squared'.

You can also use *square* as a verb.

So when you have to square –9, you have to do (–9)^{2} = 81.

### Cube

The ^{3} can be pronounced as *cube(d)*.

Therefore 7^{3} can be pronounced as: 'seven cubed'.

You can also use *cube* as a verb.

So when you have to cube –9, you have to do (–9)^{3} = –729.

## Examples

*Numerical examples with an intermediate step**

5^{2} = 5 × 5 = 25

–5^{2} = –(5 × 5) = –25

(–5)^{2} = –5 × –5 = 25

8^{3} = 8 × 8 × 8 = 512

–8^{3} = –(8 × 8 × 8) = –512

(–8)^{3} = –8 × –8 × –8 = –512

* The intermediate step is not necessary to write down, however very useful for the explanation here.

*Formula examples*

A cube has edges/sides that always have the same length.

Therefore, you can make the following formulas and shorten them:

`Volume` = `side` × `side` × `side` = `s`^{3}

`Area` = 6 × `side` × `side` = 6`s`^{2}

Look for more formulas and graphs at power relation.