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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 7

Exponents and Scientific Notation

Lesson 7: Practice with Rational Bases

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Collection Math Quiz Collection: The Laws of Exponents

Overview

This collection aggregates all the math quizzes on this topic: The Laws of Exponents. There are a total of 3 resources. This collection of quizzes is made up of downloadable PDFs. To download the full set of these resources, click on this link.

 

Laws of Exponents
Math Examples Math Examples Collection: Integer and Rational Exponents

Overview

This collection aggregates all the math examples around the topic of Integer and Rational Exponents. There are a total of 15 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation.

 

To download the full set of these resources, click on this link.

 

Numerical Expressions
Exponential Collection Math Definitions Collection: Exponential and Logarithmic Vocabulary

Overview

This collection aggregates all the definition image cards around the topic of Exponential and Logarithmic vocabulary. There are a total of 11 terms. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation.

 

 

 

Applications of Exponential and Logarithmic Functions
Math Examples Math Examples Collection: The Laws of Exponents

Overview

This comprehensive collection of 24 Math Examples focuses on the Laws of Exponents, providing educators with a rich resource to enhance their lesson plans. This set of downloadable images covers a wide range of skills related to exponent manipulation.

Laws of Exponents
Closed Captioned Video: Algebra Nspirations: Exponents and Exponential Functions Closed Captioned Video: Algebra Nspirations: Exponents Closed Captioned Video: Algebra Nspirations: Exponents and Exponential Functions

Almost everyone has an intuitive understanding that exponential growth means rapid growth. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video builds on students’ intuitive notions, explores exponential notation, and analyzes properties of exponential function graphs, with the help of TI-Nspire features such as sliders and graph transformations. Using exponential functions to model finance applications and a Newton’s law of cooling problem further help students build a solid foundation for these fundamental algebraic concepts. Concepts explored: functions, exponents, exponential functions.

Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions
Closed Captioned Video: Algebra Nspirations: Exponents and Exponential Functions, Segment 3 Closed Captioned Video: Algebra Nspirations: Exponents, 3 Closed Captioned Video: Algebra Nspirations: Exponents and Exponential Functions, Segment 3

In this Investigation we look at exponential growth and decay models. This video is Segment 3 of a 4 segment series related to Exponents and Exponential Functions. Segments 3 and 4 are grouped together.

In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis.

—PRESS PREVIEW TO SEE THE VIDEO—

This is part of a collection of videos from the Algebra Applications video series on the topic of Exponential Functions.

Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions
Closed Captioned Video: Algebra Nspirations: Exponents and Exponential Functions, Segment 1 Closed Captioned Video: Algebra Nspirations: Exponents, 1 Closed Captioned Video: Algebra Nspirations: Exponents and Exponential Functions, Segment 1

In this Investigation we explore the properties of exponents and exponential graphs. This video is Segment 1 of a 4 segment series related to Exponents and Exponential Functions. Segments 1 and 2 are grouped together.

In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis.

—PRESS PREVIEW TO SEE THE VIDEO—

This is part of a collection of videos from the Algebra Applications video series on the topic of Exponential Functions.

Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Compound Interest 1 Definition--Exponential Concepts--Compound Interest 1 Definition--Exponential Concepts--Compound Interest 1

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Compound Interest 2 Definition--Exponential Concepts--Compound Interest 2 Definition--Exponential Concepts--Compound Interest 2

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Exponent Definition--Exponential Concepts--Exponent Definition--Exponential Concepts--Exponent

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Exponential Decay Definition--Exponential Concepts--Exponential Decay Definition--Exponential Concepts--Exponential Decay

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Exponential Equation Definition--Exponential Concepts--Exponential Equation Definition--Exponential Concepts--Exponential Equation

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Exponential Function Definition--Exponential Concepts--Exponential Function Definition--Exponential Concepts--Exponential Function

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Exponential Growth Definition--Exponential Concepts--Exponential Growth Definition--Exponential Concepts--Exponential Growth

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Exponential Models Definition--Exponential Concepts--Exponential Models Definition--Exponential Concepts--Exponential Models

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Graphs of Exponential Functions Definition--Exponential Concepts--Graphs of Exponential Functions Definition--Exponential Concepts--Graphs of Exponential Functions

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Inverse of an Exponential Function Definition--Exponential Concepts--Inverse of an Exponential Function Definition--Exponential Concepts--Inverse of an Exponential Function

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Laws of Exponents Definition--Exponential Concepts--Laws of Exponents Definition--Exponential Concepts--Laws of Exponents

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
Definition--Exponential Concepts--Laws of Exponents Definition--Exponential Concepts--Laws of Exponents Definition--Exponential Concepts--Laws of Exponents

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

Applications of Exponential and Logarithmic Functions
INSTRUCTIONAL RESOURCE: Math Examples--Laws of Exponents INSTRUCTIONAL RESOURCE: Math Examples 24 INSTRUCTIONAL RESOURCE: Math Examples--Laws of Exponents

The complete set of 24 examples that make up this set of tutorials.

This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Laws of Exponents
INSTRUCTIONAL RESOURCE: Tutorial: The Laws of Exponents INSTRUCTIONAL RESOURCE: Tutorial: The Laws of Exponents INSTRUCTIONAL RESOURCE: Tutorial: The Laws of Exponents

In this tutorial we walk students through the Laws of Exponents.

This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Laws of Exponents
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 1 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 1 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 1

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 10 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 10 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 10

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 11 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 11 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 11

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 12 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 12 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 12

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 13 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 13 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 13

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 14 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 14 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 14

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 15 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 15 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 15

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 2 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 2 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 2

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 3 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 3 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 3

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 4 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 4 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 4

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 5 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 5 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 5

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 6 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 6 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 6

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 7 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 7 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 7

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 8 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 8 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 8

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Integer and Rational Exponents--Example 9 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 9 Math Example--Exponential Concepts--Integer and Rational Exponents--Example 9

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Numerical Expressions
Math Example--Exponential Concepts--Laws of Exponents: Example 1 Math Example--Exponential Concepts--Laws of Exponents: Example 1 Math Example--Exponential Concepts--Laws of Exponents: Example 1

Topic

Exponents

Description

This example demonstrates the simplification of an expression using the laws of exponents. The problem involves simplifying x2 * x3, which results in x5 by applying the law of exponents for multiplication. This step-by-step solution helps students understand how to combine like terms with exponents.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 10 Math Example--Exponential Concepts--Laws of Exponents: Example 10 Math Example--Exponential Concepts--Laws of Exponents: Example 10

Topic

Exponents

Description

This example focuses on simplifying an expression with both positive and negative exponents. The problem involves simplifying x3 * x(-5) * x(-3), which results in x(-5) or 1/x5. This demonstrates how positive and negative exponents interact when multiplying terms with the same base, and how the result can be expressed as a fraction.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 11 Math Example--Exponential Concepts--Laws of Exponents: Example 11 Math Example--Exponential Concepts--Laws of Exponents: Example 11

Topic

Exponents

Description

This example demonstrates the simplification of an expression with both positive and negative exponents, including a zero exponent. The problem involves simplifying x(-10) * x10 * x(-2), which results in x(-2) or 1/x2. This showcases how positive and negative exponents interact when multiplying terms with the same base, and how zero exponents affect the result.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 12 Math Example--Exponential Concepts--Laws of Exponents: Example 12 Math Example--Exponential Concepts--Laws of Exponents: Example 12

Topic

Exponents

Description

This example focuses on simplifying an expression with multiple negative exponents. The problem involves simplifying x(-1) * x(-5) * x(-3), which results in x(-9) or 1/x9. This demonstrates how negative exponents interact when multiplying terms with the same base, and how the result can be expressed as a fraction with a positive exponent in the denominator.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 13 Math Example--Exponential Concepts--Laws of Exponents: Example 13 Math Example--Exponential Concepts--Laws of Exponents: Example 13

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving division with exponents. The problem involves simplifying x3 / x2, which results in x. This showcases how exponents behave when dividing terms with the same base, illustrating the subtraction of exponents in division.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 14 Math Example--Exponential Concepts--Laws of Exponents: Example 14 Math Example--Exponential Concepts--Laws of Exponents: Example 14

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving division with negative exponents. The problem involves simplifying x(-5) / x6, which results in x(-11) or 1/x11. This showcases how negative and positive exponents interact when dividing terms with the same base, and how the result can be expressed as a fraction.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 15 Math Example--Exponential Concepts--Laws of Exponents: Example 15 Math Example--Exponential Concepts--Laws of Exponents: Example 15

Topic

Exponents

Description

This example illustrates the simplification of an expression involving division with both positive and negative exponents. The problem involves simplifying x8 / x(-4), which results in x12. This demonstrates how positive and negative exponents interact when dividing terms with the same base, and how the result can yield a larger positive exponent.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 16 Math Example--Exponential Concepts--Laws of Exponents: Example 16 Math Example--Exponential Concepts--Laws of Exponents: Example 16

Topic

Exponents

Description

This example focuses on simplifying an expression with negative exponents in both the numerator and denominator. The problem involves simplifying x(-7) / x(-5), which results in x(-2) or 1/x2. This demonstrates how negative exponents interact when dividing terms with the same base, and how the result can be expressed as a fraction.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 17 Math Example--Exponential Concepts--Laws of Exponents: Example 17 Math Example--Exponential Concepts--Laws of Exponents: Example 17

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with exponents. The problem involves simplifying (x2 * x3) / x4, which results in x. This showcases how exponents behave when multiplying and dividing terms with the same base, illustrating the addition and subtraction of exponents in a single expression.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 18 Math Example--Exponential Concepts--Laws of Exponents: Example 18 Math Example--Exponential Concepts--Laws of Exponents: Example 18

Topic

Exponents

Description

This example focuses on simplifying an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x-3 * x5) / x6, which results in x-4 or 1/x4. This demonstrates how positive and negative exponents interact when multiplying and dividing terms with the same base, and how the result can be expressed as a fraction.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 19 Math Example--Exponential Concepts--Laws of Exponents: Example 19 Math Example--Exponential Concepts--Laws of Exponents: Example 19

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x6 * x-10) / x2, which results in x-6 or 1/x6. This showcases how positive and negative exponents interact when multiplying and dividing terms with the same base, and how the result can be expressed as a fraction.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 2 Math Example--Exponential Concepts--Laws of Exponents: Example 2 Math Example--Exponential Concepts--Laws of Exponents: Example 2

Topic

Exponents

Description

This example focuses on simplifying an expression with negative exponents using exponent rules. The problem involves simplifying x(-3) * x4, which results in x1 or simply x. This demonstrates how positive and negative exponents interact when multiplying terms with the same base.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 20 Math Example--Exponential Concepts--Laws of Exponents: Example 20 Math Example--Exponential Concepts--Laws of Exponents: Example 20

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x5 * x9) / x-6, which results in x20. This showcases how positive and negative exponents interact when multiplying and dividing terms with the same base, and how dividing by a negative exponent can lead to a larger positive exponent.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 21 Math Example--Exponential Concepts--Laws of Exponents: Example 21 Math Example--Exponential Concepts--Laws of Exponents: Example 21

Topic

Exponents

Description

This example focuses on simplifying an expression involving multiplication and division with negative exponents. The problem involves simplifying (x(-3) * x(-5)) / x5, which results in 1/x13. This demonstrates how negative exponents interact when multiplying and dividing terms with the same base, and how the result can be expressed as a fraction with a positive exponent in the denominator.

Laws of Exponents