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Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn about zero and negative exponents.

New York State Common Core Math Grade 8, Module 1, Lesson 4 and lesson 5.

Download Worksheet for Common Core Grade 8, Module 1, Lesson 4

Download Worksheet for Common Core Grade 8, Module 1, Lesson 5

Lesson 4 Student Outcomes

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn about zero and negative exponents.

New York State Common Core Math Grade 8, Module 1, Lesson 4 and lesson 5.

Download Worksheet for Common Core Grade 8, Module 1, Lesson 4

Download Worksheet for Common Core Grade 8, Module 1, Lesson 5

Lesson 4 Student Outcomes

Students know that a number raised to the zeroth power is equal to one.

Students recognize the need for the definition to preserve the properties of exponents.

Lesson 4 Opening Exercise

For any numbers x, y and any positive integers m, n, the following holds:

x^{m} • x^{n} = x^{m+n}

(x^{m})^{n }= x^{mn}

(xy)^{n} = x^{n}y^{n}

Definition: For any positive number x, we define x^{0} = 1.

Examples

1. Simplify the following expression as much as possible.

9^{15 }• 9^{-10} • 9^{-5} =

4^{10}/4^{10} • 7^{0} =

Lesson 5 Student Outcomes

Students know the definition of a number raised to a negative exponent.

Students simplify and write equivalent expressions that contain negative exponents.

Lesson 5 Opening Exercise

For any numbers x, y and any positive integers m, n, the following holds:

x^{m} • x^{n} = x^{m+n}

(x^{m})^{n }= x^{mn}

(xy)^{n} = x^{n}y^{n}

Definition: For any positive number x and for any positive integer n, we define x^{-n} = 1/x^{n}.

Note that this definition of negative exponents says x^{-1} is just the reciprocal 1/x of x.

x^{m} ÷ x^{n} = x^{m-n}

(x/y)^{n} = x^{n}/y^{n}

Examples

2^{-1} =

3^{-2} =

(4/5)^{-3} =

5^{-2} =

1/8^{9} =

3 • 2^{-4 }=

Let x and y be non-zero numbers

x^{-3} =

1/x^{9} =

xy
^{-4}
=

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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