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*Contributor: Erika Wargo. Lesson ID: 12453*

What's a shorter way to write 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5? Once you learn the shortcut way to write a multiplication problem when the numbers are the same, you'll be a proponent of exponents!

categories

subject

Math

learning style

Visual

personality style

Lion, Beaver

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

Multiplication is a faster way to *add* numbers together when they are all the same, such as 4 + 4 + 4, which is the same as 3 x 4. But how would you quickly *multiply* numbers together that are the same, such as 4 x 4 x 4?

- Did you know there is a way to abbreviate multiplication?

Instead of writing out long multiplication problems involving the same number, you can write them in a shorter way using *exponents*.

As you watch an example of doubling numbers and how it relates to exponents*, think about and write down answers to these questions:

- What happens when you double a number?
- What pattern do you notice when numbers are doubled? Write down the pattern you see in the video.
- How many times did the lily pads double to make it across the water?
- How can the idea of doubling be applied to your life?

*Think about these questions as you watch Cyberchase’s Lily Pad Escape, by PBS LearningMedia. Discuss the questions above with a parent or teacher.

Repeated addition is shown using multiplication. Repeated multiplication is shown using exponents. There are two parts to an expression that uses exponents: the *base* and a *power*. Look at the figure below:

The base is **2**. The base is the number that is repeatedly multiplied.

The exponent is **3**. The exponent tells how many times to multiply the base times itself. Notice how the exponent is written up higher and not directly next to the base number of **2**.

**Important** Do *not* multiply the base and the exponent together!

Expressions with exponents are read in a special way. Read the base number first, then the exponent as “to the ____ power.”

Notice how an expression with an exponent of 2 can be read as “squared” and an exponent of 3 can be read as "cubed."

2^{2} |
"two to the second power" |
2 x 2 |

2^{3} |
"two to the third power" OR"two cubed" |
2 x 2 x 2 |

2^{4} |
"two to the fourth power" | 2 x 2 x 2 x 2 |

2^{10} |
"two to the tenth power" | 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 |

Before looking at some examples, let’s review the following as you watch *Shmoop Sidebar: Exponents *from Shmoop:

- What do exponents do to the value of a number?
- What happens when you raise a number to a power of 1?
- What happens when you raise a number to a power of 0?

Review the examples below and discuss with a parent or teacher:

**Example 1** Evaluate the expression 2^{3}.

The expression 2^{3} really means 2 x 2 x 2. To evaluate the expression, multiply three 2s, which is 8.

2 x 2 equals 4 and 4 x 2 equals 8. If you multiply the base and exponent together, you will get an incorrect answer of 6.

**Example 2** Write the expression 5 x 5 x 5 x 5 in exponential form.

*Exponential form* means to write the expression with a base and exponent.

The number being repeated is 5, so the base is 5.

The 5 is repeated 4 times, so the exponent is 4.

5 x 5 x 5 x 5 = 5^{4} = five to the fourth power

**Example 3** Use a calculator to evaluate the expression 2^{6}.

2^{6} = 2 x 2 x 2 x 2 x 2 x 2 = 64

When using a calculator, there might be an exponent button, or you can type in the problem as repeated multiplication. Enter 2 x 2 x 2 x 2 x 2 x 2 and get your solution. Clear the calculator and do it again. If you did not get the same answer, solve the problem again in the calculator. Although a calculator may do most of the work for you, you need to use it very carefully and be sure you typed in the numbers correctly.

Discuss with a parent or teacher:

- In the expression 5
^{8}, which number is the base and which is the exponent? - Read the following expressions to a parent or adult: 2
^{2}, 5^{3}, 1^{100}.

In the *Got It?* section, you will practice finding, writing, and evaluating expressions with exponents as you play games.