Name Class Date 6-1 - d2ct263enury6r.cloudfront.net

1 name Class date 6-1. Integer Exponents Going Deeper Essential question: How can you develop and use the properties of integer exponents? prep for Video Tutor 1 EXPLORE Using Patterns of Integer Exponents The table below shows powers of 5, 4, and 3. 4 = 625. 5 3 = 125. 5 2 = 25. 5 1 = 5. 5 0 =. 5 -1. 5 = -2. 5 =. 4 = 256. 4 3 = 64. 4 2 = 16. 4 1 = 4. 4 0 =. 4 -1. 4 = -2. 4 =. 4 = 81. 3 3 = 27. 3 2 = 9. 3 1 = 3. 3 0 =. 3 -1. 3 = -2. 3 =. A What pattern do you see in the powers of 5? B What pattern do you see in the powers of 4? Houghton Mifflin Harcourt Publishing Company C Complete the table for the values of 50 , 5-1. , 5-2.. D Complete the table for the values of 40 , 4-1.

2 , 4-2.. E Complete the table for the values of 30 , 3-1. , 3-2.. F Conjecture Write a general rule for the values of a0 and a -n based on the patterns in the table. REFLECT. 0 and a-n 1a. Do the general rules you wrote in Part F for a apply when a = 0? Explain. Chapter 6 321 Lesson 1. prep for 2 EXPLORE Applying Properties of Integer Exponents A Complete the following equations. 3 3 3 3 3 = 3 . (3 3 3 3) 3 = 3 3 = 3 . (3 3 3) (3 3) = 3 3 = 3 . What pattern do you see when multiplying two powers with the same base? Use your pattern to complete this equation: 52 5 5 = 5 . Conjecture Write a general rule for the result of a m an . 5 1 1 1. B Complete the following equation: __ 4 4 4.

3 4 = 4_____ 4 4 4 4 . = 4_____ 4 = 4 4 = 4 . 3. 4 4 4 4 41 41 4 1. What pattern do you see when dividing two powers with the same base? 8. 63 = 6 . Use your pattern to complete this equation: __ . 6 . Houghton Mifflin Harcourt Publishing Company m a n . Conjecture Write a general rule for the result of ___. a . C Complete the following equations: 2. ( 53 ) = (5 5 5). = (5 5 5) (5 5 5). = 5 . What pattern do you see when raising a power to a power? 4. Use your pattern to complete this equation: ( 72 ) = 7 . n Conjecture Write a general rule for the result of ( am ) . Chapter 6 322 Lesson 1. REFLECT. 2a. Do the general rules you wrote in Parts A, B, and C apply if a = 0? Explain.

4 (Assume m and n are not 0.). prep for 3 EXAMPLE Applying Properties of Integer Exponents Simplify each expression. A (5 - 2) 5 3-8. + (5 + 2) 0 . (5 - 2) 5 3-8. + (5 + 2) 0 Follow the order of operations. 5 0. ( ) 3-8 +. ( ). Simplify within parentheses. 3 + Use properties of exponents. 3 + Simplify. ____. 1. + Add. 1 ____. 1.. B (10 - 6) 3 42 + (10 + 2) 2 . Houghton Mifflin Harcourt Publishing Company (10 - 6) 3 42 + (10 + 2) 2 Follow the order of operations. 3 2. ( ) 42 +. ( ). Simplify within parentheses. 4 + Use properties of exponents. 4 + Simplify. + Add. REFLECT. 3a. Describe a different method you could use to simplify each expression above that does not use properties of exponents.

5 Chapter 6 323 Lesson 1. pra c t i c e Find the value of each power. 1. 7-2. 2. 15 0 3. 10 -3 . 4. 2-5. 5. 5 -3 6. 73 . Use properties of integers to write an equivalent expression. 7. 15 2 15 -5 20 13 8. ____ 14 4 9. ___. 20 10 14 9 . 16 3. 10. ( 83 ) 11. ( 12 -5 ) 12. 4 -8 4-16.. 13. m m4 r9 14. __. -3. 15. ( a3 ) . r6 . Find the missing exponent. ( ). 4. 5. 16. b b2 = b8 x 17. _____ = x-2. 18. n = n0 . x Simplify each expression. 19. ( 2 + 4 )2 + 8-6. ( 12 - 4 )10.. ( Houghton Mifflin Harcourt Publishing Company ). 3. 2 (5 - 2 ) . 20. ( 33 ) _____. 4 + ( 10 - 4 )2 6 10 . 3 . 3. 4 3 as __. 21. Error Analysis A student simplified the expression ___ 1 . Do you agree with 16 4.

6 The student? Justify your answer. x 5 . What do you notice about the two values? and __. 22. Find the values of x 5 x -3. x 3 . Explain why your results make sense based on the properties you learned in this lesson. Chapter 6 324 Lesson 1. name Class date _____. name _____ date Class_____ 6-1. Practice Additional Practice LESSON. 6-1. Integer Exponents Simplify. 1 1 1 1. 1. 5 3 2. 2 6. ___ _____ ___ _____. _____ _____. 3. ( 5) 2 4. (4) 3. _____ _____. 5. 60 6. (7) 2. _____ _____. Evaluate each expression for the given value(s) of the variable(s). 7. d 3 for d 2 8. a5b 6 for a 3 and b 2 9. (b 4) 2 for b 1. _____ _____ _____. x x 10. 5z for z 3 and x 2 11. (5z) for z 3 and x 2 12.

7 C 3 (16 2) for c 4. _____ _____ _____. Simplify. s 3. 13. t 4 14. 3r 5 15. t 5. _____ _____ _____. Houghton Mifflin Harcourt Publishing Company h0 2x 3 y 2 4fg 5. 16. 17. 18. 3 z4 5h 3. _____ _____ _____. 14a 4 a 4c 2e0 3g 2 hk 2. 19. 20. 21. 20bc 1 b 1d 3 6h0. _____ _____ _____. 22. A cooking website claims to contain 105 recipes. Evaluate this expression. _____. 23. A ball bearing has diameter 2 3 inches. Evaluate this expression. _____. Chapter 6 Copyright by Holt McDougal. Additions and changes325 Original content to the original content are the responsibility of the instructor. Lesson 1. 40 Holt McDougal Algebra 1. name _____ date _____ Class _____. Problem Solving Problem Solving LESSON.

8 6-1. Integer Exponents Write the correct answer. 1. At the 2005 World Exposition in Aichi, 2. Despite their name , Northern Yellow Japan, tiny mu-chips were embedded in Bats are commonly found in warm, the admissions tickets to prevent humid areas in the southeast United counterfeiting. The mu-chip was States. An adult has a wingspan of developed by Hitachi in 2003. Its area about 14 inches and weighs between is 42(10) 2 square millimeters. Simplify 3(2) 3 and 3(2) 2 ounces. Simplify these this expression. expressions. _____ _____. 3. Saira is using the formula for the area 4. The volume of a freshwater tank can of a circle to determine the value of S. be expressed in terms of x, y, and z.

9 She is using the expression Ar 2 where Expressed in these terms, the volume A and r 4. Use a calculator of the tank is x3y 2z liters. Determine to evaluate Saira's expression to find her the volume of the tank if x 4, y 3, approximation of the value of S to the and z 6. nearest thousandth. _____ _____. Alison has an interest in entomology, the study of insects. Her collection of insects from around the world includes the four specimens shown in the table below. Select the best answer. Houghton Mifflin Harcourt Publishing Company Insect Mass 5. Cockroaches have been found on every continent, including Antarctica. What is Emperor Scorpion 2 5 kg the mass of Alison's Madagascar Hissing African Goliath Beetle 11 1 kg Cockroach expressed as a quotient?

10 Giant Weta 2 4 kg 1 1. A kg C kg Madagascar Hissing Cockroach 5 3 kg 125 15. 1. B kg D 125 kg 125. 6. Many Giant Wetas are so heavy that 7. Scorpions are closely related to spiders they cannot jump. Which expression is and horseshoe crabs. What is the mass another way to show the mass of the of Alison's Emperor Scorpion expressed specimen in Alison's collection? as a quotient? 1 1 1. F (2)4 kg H kg A kg C kg 2 2 2 2 32 32. 4 1. 1 1 B kg D 32 kg G kg J 4 kg 25. 2 2. Chapter Original 6 Copyright by Holt McDougal. Additions and changes326 content to the original content are the responsibility of the instructor. Lesson 1. 113 Holt McDougal Algebra 1.