Let us first recap the **third index law**:

**a ^{m} ÷ a^{n} = a^{m-n}**

We can use this to simplify algebraic expressions in the same way as we do when working with numbers.

This may look tricky, but it's much simpler in practise!

When dividing two (or more) numbers or variables which have the same base (big number), we can use the third index law to simplify the expressions by simply subtracting the powers.

**e.g. x ^{12 }÷ x^{6} = x^{6}**

If you have two or more numbers, we need to remember to divide them as well.

**e.g. 16b ^{8} ÷ 8b^{5} = 2b^{3}**

In this activity, we will use index laws (like the example above) to simplify algebraic expressions to make them easier to work with.