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# ZingPath: Working with Exponents and Radicals

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## Working with Exponents and Radicals

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### Lesson Focus

#### Exponents and Their Properties

Algebra Foundations

You will apply the properties of exponents to evaluate expressions.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Calculate the integer powers of real numbers.
• Apply the properties of exponents to evaluate expressions.

### Everything You'll Have Covered

In this Activity Object, students will use problem solving strategies to notice patterns and figure out how to add up integers from 1 to n.

This same problem was given to the German mathematician, Carl Gauss, when he was only 7 years old. His teacher asked the class to add up the numbers from 1 to 100. He quickly spotted a pattern to find the correct answer. Instead of computing the answer the 'long way,' Gauss added up 100 pairs of numbers, each pair totaling 101.

For example,

Gauss might have listed the numbers from 1-100:

1 + 2 + 3 + ..........+ 98 + 99 +100

Then listed the numbers backwards:

100 + 99 + 98.....+ 3 + 2 + 1

And added each pair of numbers:

1 + 100 = 101, 2 + 99=101, 3 + 98 = 101, etc.

He noticed that each pair added up to 101, so he could multiply 101 by the total amount of numbers.

101 x 100

Since he added each number twice, he divided by 2 to find the answer.

Here is the formula for the pattern:

Other important vocabulary includes:

Gauss - a German mathematician who is sometimes called the "Prince of Mathematics"

pattern - a set of numbers or objects in which all of the members in that set are related to each other by a specific rule

consecutive integers - whole numbers that follow each other in order.

For example: 1, 2, 3, 4, 5, 6...

Be sure that students are familiar with the concept of adding consecutive integers together.

### Tutorial Details

 Approximate Time 10 Minutes Pre-requisite Concepts Students should know how to multiply and divide integers. Course Algebra Foundations Type of Tutorial Concept Development Key Vocabulary base, exponent, exponential form