Suppose you have the expression:

How could you write this expression in a more concise way?

### Product Rules for Exponents

In the expression , the is called the **base** and the is called the **exponent**. Exponents are often referred to as **powers**. When an exponent is a positive whole number, it tells you how many times to multiply the base by itself. For example:

- .

There are many rules that have to do with exponents (often called the **Laws of Exponents**) that are helpful to know so that you can work with expressions and equations that involve exponents more easily. Here you will learn two rules that have to do with exponents and products.

- To multiply two terms with the same base, add the exponents.

- To raise a product to a power, raise each of the factors to the power.

#### Let's simplify the following expressions:

The answer can be taken one step further. The base is numerical so the term can be evaluated.

- .

- .

- .

### Examples

#### Example 1

Earlier, you were asked to write the following expression in a more concise way;

The expression can be rewritten as . Then, you can use the rules of exponents to simplify the expression to . This is certainly much quicker to write!

#### Example 2

Simplify the following expression:

. Here are the steps:

#### Example 3

Simplify the following expression:

. Here are the steps:

#### Example 4

Simplify the following expression:

Here are the steps:

OR

### Review

Simplify each of the following expressions, if possible.

Expand and then simplify each of the following expressions.

- Hint: Look for a pattern in the previous two problems.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.1.