Use Multiplication to Simplify Algebraic Powers

This activity is about simplifying algebraic powers using multiplication.

Example

 Simplify:

(2a³b²)⁴

Answer

Remember what to the power of 4 means and multiply the terms 4 times.

We get:    

2a³b² × 2a³b² × 2a³b² × 2a³b²

Multiply the numbers (2 × 2 × 2 × 2 = 16).

Add the indices of identical letters

(for the letter a: 3 + 3 + 3 + 3 = 12 and for the letter b: 2 + 2 + 2 + 2 = 8).

Answer is 16a¹²b⁸.

Now that you can see what is actually happening, we can use a quicker method to work these out.

All we do is to multiply the powers inside the bracket with the power outside the bracket.

a has the power of 3, so we multiply 3 by 4: 3 x 4 = 12 

b has the power of 2, so we multiply 2 by 4: 2 x 4 = 8

 a¹²b⁸.

The only part that is tricky is the whole number of 2. We can't just multiply 2 by 4, we have to do 2⁴ which is 16.

16a¹²b⁸.

Let's have a go at some questions.