- Reciprocals
- Negative Exponents
- Working with Negative Exponents

Summary:

This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.

The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.

Objectives of this module: understand the concepts of reciprocals and negative exponents, be able to work with negative exponents.

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- Reciprocals
- Negative Exponents
- Working with Negative Exponents

Two real numbers are said to be *reciprocals* of each other if their product is 1. Every nonzero real number has exactly one reciprocal, as shown in the examples below. Zero has no reciprocal.

We can use the idea of reciprocals to find a meaning for negative exponents.

Consider the product of

Thus, since the product of

We also know that

Then, since

We have used

If

Write each of the following so that only positive exponents appear.

Write each of the following using only positive exponents.

It is important to note that

The problems of Sample Set A suggest the following rule for working with exponents:

In a fraction, a *factor* can be moved from the numerator to the denominator or from the denominator to the numerator by changing the sign of the exponent.

Write each of the following so that only positive exponents appear.

Write each of the following so that only positive exponents appear.

Rewrite

Notice that we are dividing powers with the same base. We’ll proceed by using the rules of exponents.

Write

We can eliminate the denominator by moving all factors that make up the denominator to the numerator.

Find the value of

We can evaluate this expression by eliminating the negative exponents.

Rewrite

Write

Find the value of

52

Write the following expressions using only positive exponents. Assume all variables are nonzero.

1

1

For the following problems, evaluate each numerical expression.

2

24

36

63

For the following problems, write each expression so that only positive exponents appear.

1

*((Reference))* Simplify

*((Reference))* Find the sum.

*((Reference))* Find the difference.

20

*((Reference))* Simplify

*((Reference))* Find the value of

1