ExponentsBasic Operations

Objectives

• Key Concept: A power is a shorthand way of indicating repeated multiplication. A power is comprised of a base and an exponent.

• Goal: Evaluate expressions containing exponents including these:

Write as a base with an exponent

Bases and Exponents

• A power, or exponential expression consists of a base and an exponent.

• An exponential expression is simply repeated multiplication. The base is the value to be multiplied and the exponent indicates how many times to multiply the base.

• In the exponential expression , the base is 4 and the exponent is 3.

Simple Exponential Expressions

Fractional Exponential Expressions

• When writing exponential expressions with fractions, be very careful.

• Both the numerator and denominator are raised to the exponent

• Do not write as . Notice that the denominator doesn’t have the exponent. If you intend for both the numerator and denominator to be raised to the exponent, either use parentheses or place the exponent in both the numerator and denominator.

Fractional Exponential Expressions

Notice the first two examples are the same. The second step differs slightly because there are often different ways to approach a problem.

The Zero Exponent

For any nonzero real number, , .

(On your quizzes and tests, don’t be the one that thinks . It’s not!)

• Examples:

Multiplication with Exponents

To multiply a power by another number, follow these steps in this order:

1. Evaluate the power.

2. Multiply by the number.

• Example:

(Warning: Do not do this! )

Addition/Subtraction with Exponents

To add or subtract a number to/from a power, follow these steps in this order:

1. Evaluate the power.

2. Perform the addition/subtraction.

• Example:

(Warning: Do not do this! )

Putting it all together

Evaluate:

1. Always evaluate the exponent first:

2. Then perform any multiplication:

3. Then perform any addition/subtraction:

(Notice we had to find a common denominator before we could subtract)

Summary

The last slide shows the process we can use every time.

To evaluate basic exponential expressions, follow these steps:

1. Evaluate the power.

2. Perform any multiplication.

3. Perform any addition/subtraction.

(Don’t forget, you have to find a common denominator whenever you add or subtract fractions.)

Review

Review

Write as a base with an exponent.

The base is 7. The exponent is 3.