0. Exponents write numbers? How can you use exponents to The expression 3 5 is called a power. The base is 3. The exponent is 5. base 3 5 exponent ACTIVITY: Using Exponent Notation Work with a partner. a. Copy and complete the table. Power Repeated Multiplication Form Value 3) 3 3 3) 2 3) 3) 9 3) 3 3) 4 3) 5 3) 6 3) 7 b. REPEATED REASONING Describe what is meant by the expression 3) n. How can you find the value of 3) n? 2 ACTIVITY: Using Exponent Notation tion Exponents In this lesson, you will write expressions using integer exponents. evaluate expressions involving integer exponents. Work with a partner. a. The cube at the right has $3 in each of its small cubes. Write a power that represents the total amount of money in the large cube. b. Evaluate the power to find the total amount of money in the large cube. 40 Chapter 0 Exponents and Scientific Notation
3 ACTIVITY: Writing Powers as Whole Numbers Work with a partner. Write each distance as a whole number. Which numbers do you know how to write in words? For instance, in words, 0 3 is equal to one thousand. a. 0 26 meters: b. 0 2 meters: observable universe Milky Way galaxy c. 0 6 meters: d. 0 7 meters: solar system Earth e. 0 6 meters: f. 0 5 meters: length of width of Lake Erie Lake Erie shoreline Width Math Practice Analyze Givens What information is given in the poem? What are you trying to find? 4 ACTIVITY: Writing a Power Work with a partner. Write the numbers of kits, cats, sacks, and wives as powers. As I was going to St. Ives I met a man with seven wives Each wife had seven sacks Each sack had seven cats Each cat had seven kits Kits, cats, sacks, wives How many were going to St. Ives? Nursery Rhyme, 730 5. IN YOUR OWN WORDS How can you use exponents to write numbers? Give some examples of how exponents are used in real life. Use what you learned about exponents to complete Exercises 3 5 on page 44. Section 0. Exponents 4
a. 2) 4 2) 4 = 2) 2) 2) 2) Write as repeated multiplication. 0. Lesson Lesson Tutorials Key Vocabulary power, p. 42 base, p. 42 exponent, p. 42 A power is a product of repeated factors. The base of a power is the common factor. The exponent of a power indicates the number of times the base is used as a factor. base 2) 5 = power exponent 2 2 2 2 2 is used as a factor 5 times. 2 Study Tip EXAMPLE Use parentheses to write powers with negative bases. Writing Expressions Using Exponents Write each product using exponents. a. 7) 7) 7) Because 7 is used as a factor 3 times, its exponent is 3. So, 7) 7) 7) = 7) 3. b. π π r r r Because π is used as a factor 2 times, its exponent is 2. Because r is used as a factor 3 times, its exponent is 3. So, π π r r r = π 2 r 3. Exercises 3 0 Write the product using exponents.. 4 4 4 4 4 2. 0.3 0.3 0.3 0.3 x x EXAMPLE 2 Evaluating Expressions Evaluate each expression. The base is 2. = 6 Simplify. The base is 2. b. 2 4 2 4 = 2 2 2 2) Write as repeated multiplication. = 6 Simplify. 42 Chapter 0 Exponents and Scientific Notation
EXAMPLE 3 Using Order of Operations Evaluate each expression. a. 3 + 2 3 4 = 3 + 2 8 Evaluate the power. = 3 + 62 Multiply. = 65 Add. b. 3 3 8 2 2 = 27 64 2 Evaluate the powers. = 27 32 Divide. = 5 Subtract. Exercises 6 and 2 26 Evaluate the expression. 3. 5 4 4. 6) 3 5. 3 3 27 6. 9 2 5 0.5 EXAMPLE 4 Real-Life Application In sphering, a person is secured inside a small, hollow sphere that is surrounded by a larger sphere. The space between the spheres is inflated with air. What is the volume of the inflated space? You can find the radius of each sphere by dividing each diameter given in the diagram by 2. Outer Sphere Inner Sphere 2 m 3 m V = 4 3 π r 3 Write formula. V = 4 3 π r 3 = 4 3 π 3 2) 3 Substitute. = 4 3 π )3 = 4 3 π 27 8 ) Evaluate the power. = 4 3 π ) = 9 2 π Multiply. = 4 3 π So, the volume of the inflated space is 9 2 π 4 3 π = 9 6 π, or about 0 cubic meters. 7. WHAT IF? The the inner sphere is.8 meters. What is the volume of the inflated space? Section 0. Exponents 43
0. Exercises Help with Homework. NUMBER SENSE Describe the difference between 3 4 and 3) 4. 2. WHICH ONE DOESN T BELONG? Which one does not belong with the other three? Explain your reasoning. The exponent is 3. The power is 5. The base is 5. Five is used as a factor 3 times. 9+-6)=3 3+-3)= 4+-9)= 9+-)= Write the product using exponents. 3. 3 3 3 3 4. 6) 6) 5. 2) 2) 2) 6. 3 3 3 7. π π π x x x x 8. 4) 4) 4) y y 9. 6.4 6.4 6.4 6.4 b b b 0. t) t) t) t) t) 2 Evaluate the expression.. 5 2 2. 3 3. ) 6 4. 2) 6 5. 7. ERROR ANALYSIS Describe and correct the error in evaluating the expression. 2) 2 6. 9) 3 6 2 = 6) 6) = 36 8. PRIME FACTORIZATION Write the prime factorization of 675 using exponents. 9. STRUCTURE Write 4 4 4 using exponents. 4) 20. RUSSIAN DOLLS The largest doll is 2 inches tall. The height of each of the other dolls is 7 0 the height of the next larger doll. Write an expression involving a power for the height of the smallest doll. What is the height of the smallest doll? 44 Chapter 0 Exponents and Scientific Notation
3 Evaluate the expression. 2. 5 + 3 2 3 22. 2 + 7 3) 2 23. 3 2 2 2 ) 5 24. 2 43 6 3 2 ) 25. 2 7 + 53 ) 26. 2) 3 4) 2 27. MONEY You have a part-time job. One day your boss offers to pay you either 2 h or 2 h dollars for each hour h you work that day. Copy and complete the table. Which option should you choose? Explain. h 2 3 4 5 2 h 2 h 28. CARBON-4 DATING Scientists use carbon-4 dating to determine the age of a sample of organic material. a. The amount C in grams) of a 00-gram sample of carbon-4 remaining after t years is represented by the equation C = 000.99988) t. Use a calculator to find the amount of carbon-4 remaining after 4 years. b. What percent of the carbon-4 remains after 4 years? 29. The frequency in vibrations per second) of a note on a piano is represented by the equation F = 440.0595) n, where n is the number of notes above A-440. Each black or white key represents one note. A# C# D# F# G# a. How many notes do you take to travel from A-440 to A? b. What is the frequency of A? A 440 c. Describe the relationship between the number of notes between A-440 and A and the increase in frequency. B C D E F G A Tell which property is illustrated by the statement. Skills Review Handbook) 30. 8 x = x 8 3. 2 0)x = 20 x) 32. 3x ) = 3x 33. MULTIPLE CHOICE The polygons are similar. What is the value of x? Section 2.5) 27 A 5 B 6 C 7 D 36 8 24 x Section 0. Exponents 45