  Exponent Powers

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

Elementary

subject
Math
learning style
Visual
personality style
Lion, Beaver
Intermediate (3-5), Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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:

23

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."

 22 "two to the second power"    OR"two squared" 2 x 2 23 "two to the third power"    OR"two cubed" 2 x 2 x 2 24 "two to the fourth power" 2 x 2 x 2 x 2 210 "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 a short video clipo on exponents, All You Need to Know About Exponents from Shmoop University:

• 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 23.

The expression 23 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 = 54 = five to the fourth power

Example 3 Use a calculator to evaluate the expression 26.

26 = 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 58, which number is the base and which is the exponent?
• Read the following expressions to a parent or adult: 22, 53, 1100.

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

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