Understand Multiplication of Algebraic Terms with Powers

This activity is about the multiplication of algebraic terms with powers.

Example

Do the following multiplication:

Method 1

Break down what a⁹ and a³ mean and multiply them together.

We get: a × a × a × a × a × a × a × a × a × a × a × a

This can be simplified to a¹²

Method 2

The other way we can look at this is by just looking at the indices. We already know that a⁹ x a³ = a¹²

The trick to notice here is that if we are multiplying numbers written as powers, we can just add the indices.

a⁹ x a³ = a^{(9 + 3)} = a¹²

Does that make sense? Let's test it out in some questions.