# Understanding Exponents

As we begin our study of monomials, you will need to learn and understand the use of **exponents**. So, let's begin by defining the term exponent.

An **exponent** is a number (small and raised) that represents the
"shortcut method" to showing how many times a number is multiplied by
itself.

That sounds complicated, so let's look at a few examples:

## Example 1

## Example 2

Your base can even be a negative number! Take a look!

## Example 3: Negative Base

## Example 4: Another Problem With a Negative Base

## Tip!

Whenever you have a **negative base** and the **exponent** is **even**, your answer will always be **positive**!

Whenever you have a **negative base** and the **exponent** is **odd**, your answer will always be **negative**!

Now is the tricky problem! What happens when you have a negative base, but it's not in parenthesis?

## Example 5: Working with Negatives

Remember: If the "negative" is not in parentheses, you are not raising a negative number to the power. This means that you take the opposite of your final answer.

Now, I have just one more tip for you when working with exponents!

## Another Tip!

When you have a zero as an exponent, your answer will **always** be 1. The only exception is 0^{0} is undefined.

**Examples
**

**4**^{0} = 1 or 8^{0} = 1

Now it's your turn! Let's try a few practice problems to make sure you've got it!

### Practice Problems

1. 7^{2} =

2. (-8)^{2} =

3. (-9)^{3} =

4. (-3)^{4} =

5. -2^{4} =

6. -4^{3} =

### Solutions

This was just a quick review of the meaning of exponents before we
get into the laws of exponents and monomials! I hope this gives you
better foundation for beginning this unit! Good luck!

The next lesson you should check out is the laws of exponents!

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