Solve Problems Using Multiplication to Simplify Algebraic Powers

In this activity, we will be practising how to simplify algebraic powers using multiplication.

 

Example  

Simplify:

(2a³b²)⁴

 

Remember we are multiplying the bracket  like this:  

2a³b² × 2a³b² × 2a³b² × 2a³b²   = 16a¹²b⁸

 

Rather than write them out, we used a quicker method.

 

We multiplied the powers inside the bracket with the power outside the bracket.

 

 

 

So, we can see how we ended up with the answer of 16a¹²b⁸

 

In this activity, we will use this to help us with some problem type questions, like this one:

 

Question

A cube has side 2a⁵

 

 

Write an expression for the volume of the cube.

 

Answer

Before we can start working on the indices we need to know that the volume of a cube is width x height x depth.

 

We can say that (2a⁵)³ = 2³ x a^5x3

                                     = 8a¹⁵

 

Let's try some questions.