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

**Example**

Simplify:

(2a^{3}b^{2})^{4}

Remember we are multiplying the bracket like this:

2a^{3}b^{2} × 2a^{3}b^{2} × 2a^{3}b^{2} × 2a^{3}b^{2} = **16a**^{12}**b**^{8}

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 16a^{12}b^{8}

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

__Question__

A **cube** has side **2a ^{5}**

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** (2a ^{5})^{3} = 2^{3} x a^{5x3}**

** = 8a ^{15}**

Let's try some questions.