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.

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. Simply subtract the powers.

x^{12 }÷ x^{6} = x^{6}

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

16b^{8} ÷ 8b^{5} = 2b^{3}