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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, videos, and solutions to help Grade 8 students learn how to use the definition of exponential notation to make sense of the first law of exponents.

### New York State Common Core Math Grade 8, Module 1, Lesson 2

Download worksheets for Grade 8, Module 1, Lesson 2

### Lesson 2 Student Outcomes

• Students use the definition of exponential notation to make sense of the first law of exponents.

• Students see a rule for simplifying exponential expressions involving division as a consequence of the first law of exponents.

• Students write equivalent numerical and symbolic expressions using the first law of exponents.

Lesson 2 Summary

Students should state the two identities and how to write equivalent expressions for each.

Classwork

In general, if x is any number and m, n are positive integers, then x^{m} • x^{n} = x^{m + n}

Exercise 1: 14^{23} x 14^{8} =

Exercise 2: (-72)^{10} x (-72)^{13} =

Exercise 3: 5^{94} x 5^{78} =

Exercise 4: (-3)^{9} x (-3)^{5} =

Exercise 5: Let a be a number. a^{23} • a^{8} =

Exercise 6: Let f be a number. f^{10} • f^{13} =

Exercise 7: Let b be a number. b^{94} • b^{78} =

Exercise 8: Let x be a positive integer. If (-3)^{9} x (-3)^{x} = (-3)^{14}
what is x?

What would happen if there were more terms with the same base? Write an equivalent expression for each problem.

Exercise 9: 9^{4} x 9^{6} x 9^{13} =

Exercise 10: 2^{3} x 2^{5} x 2^{7} x 2^{9} =

Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not.

Exercise 11: 6^{5} x 4^{9} x 4^{3} x 6^{14} =

Exercise 12: (-4)^{2} • 17^{5} • (-4)^{3} • 17^{7} =

Exercise 13: 15^{2} x 7^{2} x 15 x 7^{4} =

Exercise 14: 2^{4} x 8^{2} =

Exercise 15: 3^{7} x 9 =

Exercise 16: 5^{4} x 2^{11} =

Exercise 17:
Let x be a number. Simplify the expression of the following number:
(2x^{3})(17x^{7}) =

Exercise 18: Let a and b be numbers. Use the distributive law to simplify the expression of the following number: a(a + b)

Exercise 19: Let a and b be numbers. Use the distributive law to simplify the expression of the following number: b(a + b)

Exercise 20: Let a and b be numbers. Use the distributive law to simplify the expression of the following number: (a + b)(a + b) In general, if x is nonzero and m, n are positive integers, then x^{m} ÷ x^{n} = x^{m - n}

Exercises 21–32

Exercise 32

Anne used an online calculator to multiply 2,000.000.000 x 2,000,000,000,000. The answer showed up on the calculator as 4e +21, as shown below. Is the answer on the calculator correct? How do you know?

Problem Set

1. A certain ball is dropped from a height of x feet, it always bounces up to 2/3 x feet. Suppose the ball is dropped from 10 feet and is caught exactly when it touches the ground after the 30th bounce, what is the total distance traveled by the ball? Express your answer in exponential notation.

2. If the same ball is dropped from 10 feet and is caught exactly at the highest point after the 25th bounce, what is the total distance traveled by the ball? Use what you learned from the last problem.

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, videos, and solutions to help Grade 8 students learn how to use the definition of exponential notation to make sense of the first law of exponents.

• Students see a rule for simplifying exponential expressions involving division as a consequence of the first law of exponents.

• Students write equivalent numerical and symbolic expressions using the first law of exponents.

Lesson 2 Summary

Students should state the two identities and how to write equivalent expressions for each.

Classwork

In general, if x is any number and m, n are positive integers, then x

Exercise 1: 14

Exercise 2: (-72)

Exercise 3: 5

Exercise 4: (-3)

Exercise 5: Let a be a number. a

Exercise 6: Let f be a number. f

Exercise 7: Let b be a number. b

Exercise 8: Let x be a positive integer. If (-3)

What would happen if there were more terms with the same base? Write an equivalent expression for each problem.

Exercise 9: 9

Exercise 10: 2

Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not.

Exercise 11: 6

Exercise 12: (-4)

Exercise 13: 15

Exercise 14: 2

Exercise 15: 3

Exercise 16: 5

Exercise 18: Let a and b be numbers. Use the distributive law to simplify the expression of the following number: a(a + b)

Exercise 19: Let a and b be numbers. Use the distributive law to simplify the expression of the following number: b(a + b)

Exercise 20: Let a and b be numbers. Use the distributive law to simplify the expression of the following number: (a + b)(a + b) In general, if x is nonzero and m, n are positive integers, then x

Exercises 21–32

Exercise 32

Anne used an online calculator to multiply 2,000.000.000 x 2,000,000,000,000. The answer showed up on the calculator as 4e +21, as shown below. Is the answer on the calculator correct? How do you know?

Problem Set

1. A certain ball is dropped from a height of x feet, it always bounces up to 2/3 x feet. Suppose the ball is dropped from 10 feet and is caught exactly when it touches the ground after the 30th bounce, what is the total distance traveled by the ball? Express your answer in exponential notation.

2. If the same ball is dropped from 10 feet and is caught exactly at the highest point after the 25th bounce, what is the total distance traveled by the ball? Use what you learned from the last problem.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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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