## How to Find the Power of a Power in Algebra

Finding a power of a power in algebra 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 in Algebra

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**, x^{2}. It consists of a**base**(x) raised to an**exponent**(2). x^{2}means x is multiplied by itself 2 times:x^{2}= x × x - This power becomes the base of another power, (x
^{2})^{3}. Here, the base is x^{2}and the exponent is 3. (x^{2})^{3}means x^{2}is multiplied by itself 3 times:(xBy writing out this in full, we see that the left hand side is equal to x multiplied by itself 6 times:^{2})^{3}= x^{2}× x^{2}× x^{2}**x**.^{6}x

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

^{2}× x^{2}× x^{2}= x × x × x × x × x × xx

^{2}× x^{2}× x^{2}= x^{6}

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

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