ACTIVITY: Finding Quotients of Powers. Quotient Repeated Multiplication Form Power
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1 10. the same base? How can you divide two powers that have 1 ACTIVITY: Finding Quotients of Powers Work with a partner. a. Copy and complete the table. Quotient Repeated Multiplication Form Power 4 ( 4) 5 ( 4) ( 5) 7 ( 5) 5 COMMON CORE Exponents In this lesson, you will divide powers with the same base. simplify expressions involving the quotient of powers. Learning Standard 8.EE b. INDUCTIVE REASONING Describe the pattern in the table. Then write a rule for dividing two powers that have the same base. a m a n = a c. Use your rule to simplify the quotients in the first column of the table above. Does your rule give the results in the third column? 4 Chapter 10 Exponents and Scientific Notation
2 Math Practice Repeat Calculations What calculations are repeated in the table? Work with a partner. How many of the smaller cubes will fit inside the larger cube? Record your results in the table. Describe the pattern in the table. a. ACTIVITY: Comparing Volumes b. s 4 s 4 s s c. d. s 6 s 6 s 10 s 10 Volume of Smaller Cube Volume of Larger Cube Larger Volume Smaller Volume Answer a. b. c. d.. IN YOUR OWN WORDS How can you divide two powers that have the same base? Give two examples of your rule. Use what you learned about dividing powers with the same base to complete Exercises 6 on page 46. Section 10. 4
3 10. Lesson Lesson Tutorials Words To divide powers with the same base, subtract their exponents. Numbers = 45 = 4 Algebra a m a n = a m n, where a 0 Common Error When dividing powers, do not divide the bases. 6 4 =, not 1. 1 a. b. c. Dividing Powers with the Same Base 6 4 = 6 4 = Simplify. ( 7) 9 ( 7) = ( 7)9 h 7 h 6 = h7 6 = ( 7) 6 Simplify. = h 1 = h Simplify. Exercises ( 8) 8 ( 8) 4 4. x 8 x Simplifying an Expression The numerator is a product of powers. Add the exponents in the numerator. Simplify 4. Write your answer as a power. 4 = 4 + Product of Powers Property = 6 Simplify. = 6 = Simplify. 44 Chapter 10 Exponents and Scientific Notation
4 Study Tip You can also simplify the expression in Example as follows. a 10 a a7 6 a 4 = a10 a 6 a 4 = a17 a 10 a = a = a 7 Simplifying an Expression Simplify a10 a a Write your answer as a power. a a 10 a a7 6 a = 4 a10 6 a7 4 = a 4 a Simplify. = a 4 + Product of Powers Property = a 7 Simplify. Exercises d 5 5 d d 9 d Real-Life Application The projected population of Tennessee in 00 is about Predict the average number of people per square mile in 00. Use a model to solve the problem. People per square mile Population in 00 = Land area = Substitute. = Rewrite. Land area: about mi = = Evaluate. So, there will be about 174 people per square mile in Tennessee in 00. Exercises 8 8. The projected population of Alabama in 00 is about.5 1. The land area of Alabama is about 17 square kilometers. Predict the average number of people per square kilometer in 00. Section
5 10. Exercises Help with Homework 1. WRITING Describe in your own words how to divide powers.. WHICH ONE DOESN T BELONG? Which quotient does not belong with the other three? Explain your reasoning. ( 10) 7 6 ( 4) ( 10) 6 ( ) (-6)= +(-)= 4+(-9)= 9+(-1)= ( )4 ( ) ( 17)5 ( 17) ( 7.9) ( 7.9) ( 6.4)8 ( 6.4) 6 π11 1. π 7 1. b 4 b 11 n n ERROR ANALYSIS Describe and correct the error in simplifying the quotient = 6 = ( 8.) ( 8.) ( 8.)4 7 ( 8.) 19. π 0 c π π c 8 c 9 k1 1. k k17 5 k 11. SOUND INTENSITY The sound intensity of a normal conversation is 10 6 times greater than the quietest noise a person can hear. The sound intensity of a jet at takeoff is times greater than the quietest noise a person can hear. How many times more intense is the sound of a jet at takeoff than the sound of a normal conversation? 46 Chapter 10 Exponents and Scientific Notation
6 4 Simplify the expression.. x w c10 d 6 5. a b4 54 b c 9 7. x15 y 9 x 8 y 8. m10 n 7 m 1 n 6 MP Player Memory (GB) Price A 1 $70 B $10 C $170 D 4 $0 E 5 $70 9. MEMORY The memory capacities and prices of five MP players are shown in the table. a. How many times more memory does MP Player D have than MP Player B? b. Do memory and price show a linear relationship? Explain. 0. CRITICAL THINKING Consider the equation 9m 9 n = 9. a. Find two numbers m and n that satisfy the equation. b. Describe the number of solutions that satisfy the equation. Explain your reasoning. 1. STARS There are about 10 4 stars in the universe. Each galaxy has approximately the same number of stars as the Milky Way galaxy. About how many galaxies are in the universe?. Find the value of x that makes true. Explain how you found your answer. 8 x x + 1 = 89 8 Milky Way galaxy stars Subtract. (Skills Review Handbook) ( 15) 5. ( 8) MULTIPLE CHOICE What is the value of x? (Skills Review Handbook) A 0 B 0 C 45 D 60 x x Section
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