  # Use Multiplication to Simplify Algebraic Powers

In this worksheet, students will use multiplication to simplify algebraic powers. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:   #### Worksheet Overview

This activity is about simplifying algebraic powers using multiplication.

Example

Simplify:

(2a3b2)4

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).

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.

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