# 6.6: Exponential Expressions

**Advanced**Created by: CK-12

**Practice**Evaluating Exponential Expressions

Can you simplify the following expression so that it has only positive exponents?

### Watch This

James Sousa: Simplify Exponential Expressions

### Guidance

The following table summarizes all of the rules for exponents.

**Laws of Exponents**

If

am×an=am+n aman=am−n (if m>n,a≠0) (am)n=amn (ab)n=anbn (ab)n=anbn (b≠0) a0=1 (a≠0) a−m=1am amn=am−−−√n=(a√n)m

#### Example A

Evaluate

**Solution:** First, rewrite with a positive exponent:

Next, evaluate the fractional exponent:

#### Example B

Simplify

**Solution:**

#### Example C

Simplify

**Solution:**

#### Concept Problem Revisited

### Vocabulary

- Base
- In an algebraic expression, the
is the variable, number, product or quotient, to which the exponent refers. Some examples are: In the expression*base*25 , ‘2’ is the base. In the expression(−3y)4 , ‘−3y ’ is the base.

- Exponent
- In an algebraic expression, the
is the number to the upper right of the base that tells how many times to multiply the base times itself. Some examples are:*exponent*

- In the expression
25 , ‘5’ is the exponent. It means to multiply 2 times itself 5 times as shown here:25=2×2×2×2×2 . - In the expression
(−3y)4 , ‘4’ is the exponent. It means to multiply−3y times itself 4 times as shown here:(−3y)4=−3y×−3y×−3y×−3y .

- Laws of Exponents
- The
are the algebra rules and formulas that tell us the operation to perform on the exponents when dealing with exponential expressions.*laws of exponents*

### Guided Practice

Use the laws of exponents to simplify each of the following:

1.

2.

3.

**Answers:**

1.

2.

3.

### Practice

Simplify each expression.

(x10)(x10) (7x3)(3x7) (x3y2)(xy3)(x5y) (x3)(x2)(x4) x2x−3 x6y8x4y−2 (2x12)3 (x5y10)7 (2x103y20)3

Express each of the following as a power of 3. Do not evaluate.

(33)5 (39)(33) (9)(37) 94 (9)(272)

Apply the laws of exponents to evaluate each of the following without using a calculator.

(23)(22) 66÷65 −(32)3 (12)3+(13)2 (13)6÷(13)8

Use the laws of exponents to simplify each of the following.

(4x)2 (−3x)3 (x3)4 (3x)(x7) (5x)(4x4) (−3x2)(−6x3) (10x8)÷(2x4)

Simplify each of the following using the laws of exponents.

512×513 (d4e8f12)14 y12xy−−√x23−−−−−−⎷4 (32a20b−15)15 (729x12y−6)23

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 6.6.

### Image Attributions

## Description

## Learning Objectives

Here you'll learn how to use all of the laws of exponents to simplify and evaluate exponential expressions.

## Related Materials

## Difficulty Level:

Advanced## Tags:

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## Date Created:

Apr 30, 2013## Last Modified:

Oct 19, 2015## Vocabulary

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