Multiply Terms Involving Index Laws

Let us first recap the index laws:

a^m × aⁿ = 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.

x⁵ × x⁶ = x¹¹

(x³)² = x³ × x³ = x⁶

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

3x⁶ × 7x³ = 21x⁹

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

(5x³)² =  5x³ × 5x³ = 5² × x⁶  = 25x⁶

Let's try some questions now.