# 2.4 Negative exponents

The same approach used to understand what zero as a power means can also be used for negative exponents or powers.

This time showing as a fraction, simplifying and using the rules for powers with the same base. This gives:

So,

Now, using the rule for dividing numbers with the same base:

Putting these two results together gives:

In the same way, means , or , which is equivalent to .

Since is 25 and is , in maths 5^{-2} is said to be the **reciprocal** of 5^{2}. So, negative powers represent the reciprocal of the same positive power.

Negative powers of ten then enable small numbers to be shown using scientific notation. Before that though you will practise understanding and writing negative powers in the next activity.

## Activity _unit6.2.4 Activity 5 Understanding and writing negative powers

Without using your calculator, write the following numbers as fractions or whole numbers, as appropriate.

Remember you can always click on ‘reveal comment’ for a hint if you get stuck.

- a.

### Answer

- a.

- b.

### Answer

- b.

- c.

### Answer

- c.

Write the following as powers of ten.

- d.0.01

### Discussion

Convert the number to a fraction first, think about place value if you need to.

### Answer

- d.

- e.0.00001

### Answer

- e.