# Index Form, Roots and Laws

An Index can sometimes also be referred to as a Power. An Index is the small number that floats beside a letter or number. Indices is the plural term for an Index.

The index number shows how many times a letter or number has been multiplied by itself, essentially telling you how many times the number or letter has been multiplied.

When you see 3^{4}**3** is the base number and** ^{4}** is the Index number. So this would indicate 3 x 3 x 3 x 3. With 3 multiplied 4 times.

**Roots can be calculated as follows:**

√25 = 5 this symbolises that the square root of 25 is 5, because 5 x 5 = 25.

^{3}√8 = 2 this symbolises that the cube root of 8 is 2, because 2 x 2 x 2 = 8.

^{4}√81 = 3 this symbolises that the fourth root of 81 is 3, because 3 x 3 x 3 x 3 = 81.

^{5}√32 = 2 this symbolises that the fifth root of 32 is 2, because 2 x 2 x 2 x 2 x 2 = 32.

Index laws will only apply if the base numbers are the same and the normal rules will also apply for negative numbers.

**To multiply indices** you simply have to **add** the powers to get the final index, for example:

3^{4} x 3^{3 }= 3^{4 + 3 }= 3^{7}

**To divide indices** you simply have to **subtract** the powers to get the final index, for example:

3^{5 }÷ 3^{3 }= 3^{5 - 3 }= 3^{2}

**To raise one power to another power** we simply have to **multiply** the powers to give the final index for example:

(3^{2})^{ 4} = 3^{2 x 4 }= 3^{8}

This video explains how to use Indices in Algebraic form.

You can find out more on working with Indices in Algebra here.