Lesson 13.1 Assignment Name Date Exponentially Speaking Powers and Exponents 1. As the principal of Hope Middle School, Mr. Williams is in charge of notifying his staff about school delays or cancellations due to weather, power outages, or other unexpected events. Mr. Williams starts a phone chain by calling three staff members. Each of these staff members then calls three more staff members, who each call three more staff members. This completes the calling list. a. Draw a tree diagram to represent the phone chain. Chapter 13 Assignments 233
Lesson 13.1 Assignment page 2 b. Excluding Mr. Williams, how many staff members are there at Hope Middle School? Explain your calculation. c. Complete the table using the information from the tree diagram you completed in part (a). Round 1 Round 2 Round 3 Round 4 Number of calls made Expanded notation Power d. Dr. Novella, superintendent of the school district, decides that she should start the phone chain instead of the school principals. She starts the calling list by calling each of the principals of the three schools in her district. The principals continue the phone chain as described previously Explain why the table in part (c) can be used to represent Dr. Novella s phone chain. e. Complete the fourth column in the table to represent the fourth round of calls in Dr. Novella s phone chain. 234 Chapter 13 Assignments
Lesson 13.1 Assignment page 3 Name Date f. How many calls are made in the fourth round? Show your work. g. Excluding Dr. Novella, how many principals and staff members are there in the entire school district? Explain your calculation. Chapter 13 Assignments 235
236 Chapter 13 Assignments
Lesson 13.2 Assignment Name Date Digital Storage Multiplying and Dividing Powers 1. Can you use the rules you previously developed to simplify the expressions 5 3? 3 4 and 4 8 6? 3 Why or why not? 2. The hertz (Hz) is a unit of frequency that represents the number of complete cycles per second. It is used to measure repeating events, both scientific and general. For instance, a clock ticks at 1 Hz. One scientific application is the electromagnetic spectrum, or the range of all possible frequencies of electromagnetic waves. The spectrum includes frequencies from everyday contexts, such as radio and TV signals, microwaves, light (infrared, visible, and ultraviolet), and X-rays. Name Frequency 1 kilohertz (khz) 1000 Hz 1 megahertz (MHz) 1000 khz 1 gigahertz (GHz) 1000 MHz 1 terahertz (THz) 1000 GHz Use powers to write a mathematical expression. Then evaluate each expression. Express your answer as a power. a. How many hertz are in 1 gigahertz? 1 terahertz? Chapter 13 Assignments 237
Lesson 13.2 Assignment page 2 b. A television channel has a frequency of 60 megahertz. What is the channel s frequency in hertz? Show your work. c. A radio station has a frequency of 100 megahertz. What is the station s frequency in hertz? Show your work. d. The frequency of a microwave is 30 gigahertz. What is the microwave s frequency in hertz? Show your work. e. The frequency of a visible ray of light is 1000 terahertz. What is the light s frequency in hertz? Show your work. f. How many times greater is the frequency of the light in part (e) than the frequency of the radio station in part (c)? Show your work. 238 Chapter 13 Assignments
Lesson 13.2 Assignment page 3 Name Date g. How many times greater is the frequency of the microwave in part (d) than the frequency of the television channel in part (b) Show your work. Chapter 13 Assignments 239
240 Chapter 13 Assignments
Lesson 13.3 Assignment Name Date Extending the Rules Zero and Negative Exponents Simplify each expression using the properties of powers. Show your work. 1. 102 2. 325 5 10 3 25 3. (6x 4 )(2x 22 ) 4. (7 26 )(7 4 ) Chapter 13 Assignments 241
Lesson 13.3 Assignment page 2 5. (4 0 )(4 23 ) 6. 52 5 22 7. 421 8. p4 2 4 p 9 9. m22 m 10. r 23 26 q22 q 6 r 24 242 Chapter 13 Assignments
Lesson 13.3 Assignment page 3 Name Date 11. When you take a picture, the camera shutter controls how much light reaches the film or the digital image sensor. The shutter speed is the amount of time, in seconds, that the shutter stays open. Write each shutter speed as a power with a negative exponent. a. 1 second b. 1 4 8 second c. 1 125 second d. 1 1000 second 12. True or False: A number raised to a negative power is always a negative number. Give an example to support your answer. 13. Give an example of a number raised to a negative exponent that is a negative number. Chapter 13 Assignments 243
244 Chapter 13 Assignments
Lesson 13.4 Assignment Name Date Let s Get Scientific! Scientific Notation Decide whether the number is written in scientific notation. If not, write the number in scientific notation. Explain your reasoning for each number. 1. 38.7 3 10 4 2. 2.56 3 10 23 3. 0.025 3 10 26 Chapter 13 Assignments 245
Lesson 13.4 Assignment page 2 4. Complete the table. Quantity Measurement in Standard Form Measurement in Scientific Notation World population in number of people (July 2009) Time for a computer to perform an operation in seconds Average fingernail thickness in inches Gallons of fresh water used in the U.S. each year Diameter of a very fine human hair in meters 6,790,000,000 0.015 0.000017 3.0 3 10 210 2.5 3 10 13 Mass of Mars in tons 7.08 3 10 20 U.S. total public debt in dollars 12,280,000,000,000 Diameter of bacteria in inches 8 3 10 26 246 Chapter 13 Assignments
Lesson 13.5 Assignment Name Date Are We There Yet? What Is the Distance? Operations with Scientific Notation 1. As the United States has developed over the last century, Americans have used increasing amounts of electricity. The total use of electricity is measured in kilowatt-hours (kwh) and is tracked by the Department of Energy. a. The total use of electricity in the United States in 1902 was about 6.03 billion kilowatt-hours. Electricity use was about 595 times greater by 2000. Calculate the total use of electricity in 2000. Use scientific notation. Show your work. Chapter 13 Assignments 247
Lesson 13.5 Assignment page 2 b. The total use of electricity in the United States was about 0.4 trillion kilowatt-hours in 1950 and about 2.8 trillion kilowatt-hours in 1990. How many times more electricity was used in 1990 than in 1950? Use scientific notation. Show your work. 248 Chapter 13 Assignments
Lesson 13.5 Assignment page 3 Name Date c. The total use of electricity in the U.S. decreased by 51 billion kilowatt-hours from 2007 to 2008. The electricity usage in 2007 was 3.924 trillion kilowatt-hours. Calculate the percent of decrease in electricity use by dividing the amount of decrease by the usage in 2007. Use scientific notation. Show your work. d. What do you think may have contributed to the decrease from 2007 to 2008? Chapter 13 Assignments 249
250 Chapter 13 Assignments
Lesson 13.6 Assignment Name Date Watch Your Step! Identifying the Properties of Powers 1. Is the equation a 4? b 2 5 (ab ) 6 an example of the Product Rule of Powers? Explain your reasoning. Identify the property or action that justifies each step to simplify the expression. 2. (24 ) 6 (2 3 ) 2 (24) 5 (2 6 ) 7 (24)6 (24) 7 5 (24) 21 (2 6 ) 5 26 (24) 1 5 64 24 5 216 3. j 2 k 23 ( j 2 ) 2 5 j 2 k 23 ( j 4 ) 5 j2 (j 4 ) k 3 5 j6 k 3 Chapter 13 Assignments 251
Lesson 13.6 Assignment page 2 4. x25 y 8 x 25 y 5 y 8 6 x 5 x 25 y 6 5 y8 x 0 y 6 5 y8 y 6 5 y 2 5. Write an expression that requires all five properties of powers to simplify. Show the steps to simplify your expression and identify the property that justifies each step. 252 Chapter 13 Assignments