This activity is about simplifying algebraic powers using multiplication.

**Example**

Simplify:

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

**Answer**

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

We get:

2a^{3}b^{2} × 2a^{3}b^{2} × 2a^{3}b^{2} × 2a^{3}b^{2}

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 **16a**^{12}**b**^{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

**a**^{12}**b**^{8}.

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

**16a**^{12}**b**^{8}.

Let's have a go at some questions.