Chapter Review. Write each expression using exponents SOLUTION: The base 6 is a factor 5 times. So, the exponent is 5.

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1 Write each expression using exponents The base 6 is a factor 5 times. So, the exponent is = The base 4 is a factor 1 time. So, the exponent is 1. 4 = x x x The base x is a factor 3 times. So the exponent is 3. x x x = x 3 x 3 4. f f g g g g ( 4) Evaluate each expression if w =, x = 4, y = 1, and z = x 2 6 f 2 g 4 Evaluate each expression esolutions Manual - Powered by Cognero Page 1

2 10. w 3 + y Adult humans have 2 5 teeth. How many teeth do adults have? So, adult humans have 32 teeth. 32 teeth 11. 2(y + z 3 ) 14. Xander ran a total of 5 3 kilometers last month. How many kilometers did he run? So, Xander ran 125 kilometers. 125 km w 4 x 2 yz Write each expression using a positive exponent = 16. ( 10) 2 or ( 10) 2 = esolutions Manual - Powered by Cognero Page 2

3 17. m 5 m 5 = 21. Write each fraction as an expression using a negative exponent other than 1. = c 5 c 5 = or or 19. ( 4) 3 ( 4) 3 = 2 6, 4 3, or y 9 y 9 = esolutions Manual - Powered by Cognero Page 3

4 ( 7) ( 7) or 4 2 or 2 4 ( 7) m 3 m 6 m One millimeter equals meter. Write the decimal using a negative exponent. 31. x 8 x x (2h 7 )(6h) 10 3 Find each product or quotient. Express using exponents h esolutions Manual - Powered by Cognero Page 4

5 33. (5a 3 )( 6a 4 ) a 36. Venus is about 10 8 kilometers from the Sun. Saturn is about 10 9 kilometers from the Sun. About how many times farther from the Sun is Saturn than Venus? To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun. So, Saturn is about 10 times further from the Sun than Venus. about 10 times Express each number in standard form or k esolutions Manual - Powered by Cognero Page 5

6 The mass of the Sun is exagrams. Express in standard form. 252,000 Express each number in scientific notation ,000 So, the mass of the Sun is 1,988,920,000,000,000 exagrams. 1,988,920,000,000,000 exagrams Evaluate each expression. Express the result in scientific notation. 46. ( )( ) esolutions Manual - Powered by Cognero Page 6

7 48. ( ) + ( ) 51. A male elephant weighs pounds. A female elephant weighs pounds. How much more does the male elephant weigh than the female elephant? Express your result in scientific notation ( ) ( ) A fin whale weighs pounds. A blue whale weighs pounds. Estimate how many more pounds the blue whale weighs than the fin whale. The blue whale weighs about pounds more than the fin whale. about pounds The male elephant weights pounds more than the female elephant lb Find each square root or cube root. = = 5 5 = = 9 9 esolutions Manual - Powered by Cognero Page 7

8 Estimate each square root or cube root to the nearest integer. The first perfect square less than 15 is 9. = 3 The first perfect square greater than 15 is 16. = 4 The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9, is closer to 4 than to 3. 4 The first perfect square less than 52 is 49. = 7 The first perfect square greater than 52 is 64. = 8 The negative square root of 52 is between the integers 7 and 8. Since 54 is closer to 49 than to 64, is closer to 7 than to The first perfect cube less than 415 is 343. = 7 The first perfect cube greater than 415 is 512. = 8 The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512, is closer to 7 than to The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by the formula, where l is the length of the pendulum. If a clock s pendulum is 8 feet long, find the period. To find the period, substitute 8 for l The first perfect cube less than 90 is 64. = 4 The first perfect cube greater than 90 is 125. = 5 The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125, is closer to 4 than to 5. The period of the pendulum is 3.14 seconds s 4 esolutions Manual - Powered by Cognero Page 8

9 Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational Since 18 =, this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational number. natural, whole, integer, rational Replace the Ο with <, >, or = to make a true statement. 65. Ο = = Since is to the right of, >. > is written as a fraction, so it is a rational number. rational cannot be written as a fraction, so it is an irrational number. 66. Ο 8 = 8.2 = Since is to the left of 8, < 8. < 67. Ο 64. irrational Since rational, this number is a rational number. 11 = = Since 11 is to the right of, 11 >. > esolutions Manual - Powered by Cognero Page 9

10 68. Ο = = Since is to the left of, <. < Solve each equation. Round to the nearest tenth, if necessary. 69. m 3 = The formula A 3.14r 2 can be used to determine the area of a circle, where A is the area and r is the distance from the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth. To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle. Substitute 700 for A in the equation A 3.14r 2. The solutions is y 2 = 5.76 Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet ft The solutions are 1.2 and , 1.2 esolutions Manual - Powered by Cognero Page 10