# Multiplication and Division of Numbers in Exponential Form

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Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades

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.

### 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 xm • xn = xm + n

Exercise 1: 1423 x 148 =
Exercise 2: (-72)10 x (-72)13 =
Exercise 3: 594 x 578 =
Exercise 4: (-3)9 x (-3)5 =
Exercise 5: Let a be a number. a23 • a8 =
Exercise 6: Let f be a number. f10 • f13 =
Exercise 7: Let b be a number. b94 • b78 =

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: 94 x 96 x 913 =
Exercise 10: 23 x 25 x 27 x 29 =

Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not.
Exercise 11: 65 x 49 x 43 x 614 =
Exercise 12: (-4)2 • 175 • (-4)3 • 177 =
Exercise 13: 152 x 72 x 15 x 74 =
Exercise 14: 24 x 82 =
Exercise 15: 37 x 9 =
Exercise 16: 54 x 211 =

Exercise 17: Let x be a number. Simplify the expression of the following number: (2x3)(17x7) =
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 xm ÷ xn = xm - 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.

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