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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 7

Exponents and Scientific Notation

Lesson 3: Powers of Powers of 10

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 1 Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 1 Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 1

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 2 Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 2 Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 2

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 3 Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 3 Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 3

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Left

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Right

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Left

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Right

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Left

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Right

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Left Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Left

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Right Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Right

This is part of a collection of math clip art images about equations and inequalities.

Applications of Equations and Inequalities
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
Math Example--Exponential Concepts--Laws of Exponents: Example 22 Math Example--Exponential Concepts--Laws of Exponents: Example 22 Math Example--Exponential Concepts--Laws of Exponents: Example 22

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 23 Math Example--Exponential Concepts--Laws of Exponents: Example 23 Math Example--Exponential Concepts--Laws of Exponents: Example 23

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 24 Math Example--Exponential Concepts--Laws of Exponents: Example 24 Math Example--Exponential Concepts--Laws of Exponents: Example 24

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 3 Math Example--Exponential Concepts--Laws of Exponents: Example 3 Math Example--Exponential Concepts--Laws of Exponents: Example 3

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 4 Math Example--Exponential Concepts--Laws of Exponents: Example 4 Math Example--Exponential Concepts--Laws of Exponents: Example 4

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 5 Math Example--Exponential Concepts--Laws of Exponents: Example 5 Math Example--Exponential Concepts--Laws of Exponents: Example 5

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 6 Math Example--Exponential Concepts--Laws of Exponents: Example 6 Math Example--Exponential Concepts--Laws of Exponents: Example 6

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 7 Math Example--Exponential Concepts--Laws of Exponents: Example 7 Math Example--Exponential Concepts--Laws of Exponents: Example 7

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.

Laws of Exponents
Math Example--Exponential Concepts--Laws of Exponents: Example 8 Math Example--Exponential Concepts--Laws of Exponents: Example 8 Math Example--Exponential Concepts--Laws of Exponents: Example 8

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.

Laws of Exponents