Illustrative Math Alignment: Grade 8 Unit 7

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(-7)) / x(-9), which results in x8. 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 positive result.

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(-5) * x9) / x(-6), which results in x10. This demonstrates 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.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with negative exponents. The problem involves simplifying (x(-2) * x(-6)) / x(-8), which results in 1. This showcases how negative exponents interact when multiplying and dividing terms with the same base, and how they can cancel out to yield a result of 1.

Topic

Exponents

Description

This example demonstrates the simplification of an expression resulting in a negative exponent. The problem involves simplifying x5 * x(-6), which results in x(-1) or 1/x. This showcases how positive and negative exponents interact and how the result can be expressed as a fraction.

Topic

Exponents

Description

This example focuses on simplifying an expression with two negative exponents, resulting in a fraction. The problem involves simplifying x(-10) * x(-7), which results in x(-17) or 1/x17. This demonstrates how negative exponents combine and how the result can be expressed as a fraction with a positive exponent.

Topic

Exponents

Description

This example demonstrates the simplification of an expression using exponents with multiple terms. The problem involves simplifying x4 * x6 * x8, which results in x18. This showcases how the exponents of terms with the same base can be added when multiplying.

Topic

Exponents

Description

This example focuses on simplifying an expression with both negative and positive exponents. The problem involves simplifying x(-2) * x7 * x11, which results in x16. This demonstrates how positive and negative exponents interact when multiplying terms with the same base, and how they can be combined to yield a single positive exponent.

Topic

Exponents

Description

This example demonstrates the simplification of an expression using both positive and negative exponents. The problem involves simplifying x8 * x(-5) * x6, which results in x9. This showcases how positive and negative exponents interact when multiplying terms with the same base, and how they can be combined to yield a single positive exponent.

Topic

Exponents

Description

This example focuses on simplifying an expression with negative exponents and converting it to a fraction. The problem involves simplifying x2 * x * x(-5), which results in 1/x2. 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.

Topic

Exponents

Description

This example demonstrates the simplification of an expression with multiple negative exponents and one positive exponent. The problem involves simplifying x(-6) * x(-5) * x7, which results in x(-4) or 1/x4. This showcases how positive and negative exponents interact when multiplying terms with the same base, and how the result can be expressed as a fraction.

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

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

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

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

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

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

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

This Teacher's Guide provides an overview of the 24 worked-out examples on the laws of exponents.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

This is part of a collection of math quizzes on the topic of the Laws of Exponents.

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Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of the Laws of Exponents.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of the Laws of Exponents.

Related Resources

Quiz Library

ary">click on this link.

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: In this introductory segment students learn about the great earthquake of 2008 that hit the Sichuan province of China. In the process they learn about how exponential functions provide a good model for describing earthquake intensity.

This is the transcript for the video of same title. Video contents: The basic definition of an exponential function is shown in the intensity function for an earthquake. Students analyze data and perform an exponential regression based on data from the Sichuan earthquake.

This is the transcript for the video of same title. Video contents: An exponential model describes the intensity of an earthquake, while a logarithmic model describes the magnitude of an earthquake. In the process students learn about the inverse of an exponential function.

This is the transcript for the video of same title. Video contents: An earthquake is an example of a seismic wave. A wave can be modeled with a trigonometric function. Using the TI-Nspire, students link the amplitude to an exponential function to analyze the dramatic increase in intensity resulting from minor changes to magnitude.

This is the transcript for the video of same title. Video contents: 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

This is the transcript for the video of same title. Video contents: In this Investigation we explore the properties of exponents and exponential graphs.

This is the transcript for the video of same title. Video contents: In this Investigation we look at exponential growth and decay models.

Topic

Exponential Functions

Topic

Exponential Functions

Topic

Exponential Functions

Description

In this Math Lab explore a quadratic graph and an exponential graph and analyze their respective equations.

This video is relevant to the topic of Exponential Functions as it provides a detailed exploration of key concepts and their applications. By presenting clear and practical examples, it helps students understand and apply mathematical principles effectively.

Topic

Exponential Functions

Topic

Exponential Functions

Description

In this Math Lab explore cooling curves expressed as exponential functions.

This video is relevant to the topic of Exponential Functions as it provides a detailed exploration of key concepts and their applications. By presenting clear and practical examples, it helps students understand and apply mathematical principles effectively.