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Simplifying Fractions 3
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Writing Fractions as Percents
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Adding and Subtracting Fractions
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Example 6
Dividing Monomials
Multiplication can Increase or Decrease a Number
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Powers of i
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Slope of a Line
Percent Introduced
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The Hyperbola
Standard Form for the Equation of a Line
Multiplication by 75
Solving Quadratic Equations Using the Quadratic Formula
Raising a Product to a Power
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Monomial Factors
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Division Property of Square and Cube Roots
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Equations of Circles
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Integral Exponents
Linear Equations - Positive and Negative Slopes
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Basic Algebraic Operations and Simplification
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Axis of Symmetry and Vertices
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Simple Trinomials as Products of Binomials
Solving Nonlinear Equations by Factoring
Solving System of Equations
Exponential Functions
Computing the Area of Circles
The Standard Form of a Quadratic Equation
The Discriminant
Dividing Monomials Using the Quotient Rule
Squaring a Difference
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Adding Fractions
Powers of Radical Expressions
Steps for Solving Linear Equations
Quadratic Expressions Complete Squares
Fractions 1
Properties of Negative Exponents
Factoring Perfect Square Trinomials
Solving Quadratic Equations Using the Square Root Property
Dividing Rational Expressions
Quadratic Equations with Imaginary Solutions
Factoring Trinomials Using Patterns
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Integer Exponents

As we have seen, a positive integer exponent indicates repeated multiplication of a number.

For example, 45 indicates five factors, and each factor is 4.

• The base, 4, is the repeated factor.

• The exponent, 5, indicates the number of times the base appears as a factor.

The base can also be a variable, as in x6.

The exponent can also be a variable, as in xn.

Example 1

For each of the following, identify the base and the exponent. Then simplify:


a. The base is 3 and the exponent is 4. 34 indicates 4 factors. Each is 3. 34

= 3 · 3 · 3 · 3 = 81

b. The base is and the exponent is 2. There are two factors. Each is .
c. The base is 2w and the exponent is 3. There are three factors. Each is 2w. (2w)3

= (2w) · (2w) · (2w)

= (2 · 2 · 2) · (w · w · w)

= 8w3

In 2w6, the base is w:

2w6 = 2 · w · w · w · w · w · w

In (2w)6, the base is 2w:

(2w)6 = 2w · 2w · 2w · 2w · 2w · 2w

Therefore,(2w)3 = 8w3.

d. Because there are no parentheses in the expression 2w6, the base is w, not 2w. The exponent, 6, does not affect the 2. Thus, 2w6 cannot be simplified.

e. In -24, the base is 2, not -2. The exponent is 4. Thus, there are four factors. Each is 2. -24

= -(2 · 2 · 2 · 2)

= -16

Here's a different example. In this case, the base is negative two:

(-2)4 = (-2)(-2)(-2)(-2) = +16


Now, let’s look at exponents of 1 and 0, and negative exponents.

• If an exponent is 1, then the base can be written without an exponent. For example, 51 = 5 and x1 = x.

• If an exponent is 0, then the value of the expression is 1. For example, 50 = 1 and x0 = 1 (here, x 0).

• A negative exponent indicates a fraction. For example, . In general, (here, x 0).

It is also true that

For example,

Example 2

Find: 2-1(3x)0y1

Solution 2-1(3x)0y1
The factor 2-1 can be written as a fraction.

The factor (3x)0 can be written as 1.


The factor y1 can be written as y.


Thus, the result is .

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