### Guidance

Sometimes, we have to multiply the same number several times. We can say that we are multiplying the number by itself in this case.

When we have a situation like this, it is helpful to use a little number to show how many times to multiply the number by itself. That little number is called an *exponent.*

If we were going to write

Using exponents has an even fancier name too. We can say that we use ** exponential notation** when we express multiplication in terms of exponents.

We can use ** exponential notation** to write an expanded multiplication problem into a form with an exponent, we write

We can work the other way around too. We can write a number with an exponent as a long multiplication problem and this is called *expanded form.*

The ** base** is the number being multiplied by itself in this case the base is 4.

The ** exponent** tells how many times to multiply the base by itself in this case, it is a 3.

Using an exponent can also be called “raising to a power.” The exponent represents the power.

**Here 43 would be read as “Four to the third power.”**

Write the following in exponential notation:

**Exponential Notation means to write this as a base with an exponent.**

**Six times itself four times**

**This is our answer.**

Write the following in expanded form:

**Expanded form means to write this out as a multiplication problem.**

**This is our answer.**

**We can also evaluate expressions with variables.**

**Our first step is to write it out into expanded form.**

**Now multiply.**

**Our answer is 64.**

Now it's time for you to try a few on your own.

#### Example A

Write the following in exponential form:

**Solution: 35**

#### Example B

Write the following in expanded form and evaluate the expression:

**Solution: 6×6×6**

#### Example C

Evaluate:

**Solution: 39**

### Vocabulary

- Exponent
- a little number that tells you how many times to multiply the base by itself.

- Base
- the big number in a variable expression with an exponent.

- Exponential Notation
- writing long multiplication using a base and an exponent

- Expanded Form
- taking a base and an exponent and writing it out as a long multiplication problem.

### Guided Practice

Here is one for you to try on your own.

**Answer**

To evaluate this expression write it out in expanded form.

Now multiply each part of the expression.

**Our answer is 24.**

### Video Review

Here is a video for review.

- This is a James Sousa video about writing numbers in exponential form.

### Practice

Directions: Name the base and exponent in the following examples. Then write each in expanded form.

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