Let us first recap the index laws:

**a ^{m} × a^{n} = a^{m+n}**

**(a ^{m})^{n} = a^{m×n}**

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

When multiplying two (or more!) numbers or variables which have the same base (big number), we can use index laws to simplify the expressions. To simplify, just **add the indices.**

x^{5 }× x^{6} = x^{11}

(x^{3})^{2} = x^{3} × x^{3} = x^{6}

If you have two or more numbers, you should multiply them out first.

3x^{6} × 7x^{3} = 21x^{9}

If the expression that you are simplifying consists also of numbers, you might need to apply the power to that number.

(5x^{3})^{2} = 5x^{3} × 5x^{3} = 5^{2 }× x^{6 }= 25x^{6}

Let's try some questions now.