## How to Find the Power of a Power

Finding a power of a power is easy.## Question

Use the law of exponents to find the power of the power below.## Step-by-Step:

## 1

Find the exponents. In our example, the exponents are

**2**and**3**.## 2

Multiply the exponents together.

2 × 3 = 6

## 3

Make the answer from

**Step 2**(6) the exponent of the base that has been raised to the exponent.## Answer:

We have found the power of the power.## Understanding Powers of a Power

Let us look at the rule for finding a power of a power, using the example above: Firstly, let us look at what is to the left of the equals sign (=):- Inside the brackets is a
**power**, 2^{2}. It consists of a**base**(2) raised to an**exponent**(2). 2^{2}means 2 is multiplied by itself 2 times:2^{2}= 2 × 2 - This power becomes the base of another power, (2
^{2})^{3}. Here, the base is 2^{2}and the exponent is 3. (2^{2})^{3}means 2^{2}is multiplied by itself 3 times:(2By writing out this in full, we see that the left hand side is equal to 2 multiplied by itself 6 times:^{2})^{3}= 2^{2}× 2^{2}× 2^{2}**2**.^{6}2

^{2}× 2^{2}× 2^{2}= (2 × 2) × (2 × 2) × (2 × 2)2

^{2}× 2^{2}× 2^{2}= 2 × 2 × 2 × 2 × 2 × 22

^{2}× 2^{2}× 2^{2}= 2^{6}

- 2
^{2 × 3}is a power. It consists of a base (2) raised to an exponent (2 × 3). Clearly, 2^{2 × 3}is equal to**2**. The left hand side of the equation equals the right hand side.^{6}

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