## What you need to know

**Things to remember:**

- We can write negative exponents as fractions with a numerator of 1, and a denominator of the original number and power without the negative.

Powers can come in all shapes and sizes, from integers to fractions and decimals, positive numbers to negative numbers, and real numbers to imaginary…………………. but you don’t need to worry about imaginary numbers…

For example, we could see powers like this:

5^4

5^{-4}

5^{0.4}

5^{\dfrac{1}{4}}

Before we can look at negative powers, we need to remember what a **reciprocal** of a number is. The **reciprocal** of a number is the number multiply it by to make 1.

2\times\frac{1}{2}=1

6\times\frac{1}{6}=1

10\times\frac{1}{10}=1

So, to make the **reciprocal** of a number, we just write it as a fraction with a 1 on top!

Changing the negative exponent into a nicer form takes two steps:

**Step 1: **Remove the negative symbol.

**Step 2: **Write as a reciprocal of the number and power.

Exponent **Step 1 Step 2**

5^{-3} 5^{3} \dfrac{1}{5^3}

6^{-7} 6^{7} \dfrac{1}{6^7}

2^{-9} 2^{9} \dfrac{1}{2^9}

## KS3 Maths Revision Cards

(77 Reviews) £8.99## Example Questions

**Question 1:** Express 11^{-19} so it has a positive exponent.

Exponent

11^{-19}

**Step 1**

11^{19}

**Step 2**

\dfrac{1}{11^19}

11^{-19}=\frac{1}{11^{19}}

**Question 2:** Express 27^{-4} so it has a positive exponent.

Exponent

27^{-4}

**Step 1 **

27^{4}

**Step 2**

\dfrac{1}{27^4}

27^{-4}=\frac{1}{27^4}

## KS3 Maths Revision Cards

(77 Reviews) £8.99- All of the major KS2 Maths SATs topics covered
- Practice questions and answers on every topic

- Detailed model solutions for every question
- Suitable for students of all abilities.