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Evaluate the expression. Tell which properties of exponents you used.

1. 25. 23 2. (-7i( -7)

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Simplify the expression. Tell which properties of exponents you used.

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21. (40w2)-5 22. (y4z2)(y-3z-5) 23. (2m3n-I)(8m4n-2)

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Write an expression for the surface area or volume in terms of x.

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33. 'Birds Some scientists estimate that there are about 8600 species of birds in theworld. The mean number of birds per species is approximately 12,000,000. About,how Many birds are there in the world? Write your answer in scientific notation.

34. Biology A red blood cell has a diameter of approximately 0.00075 centimeter. Ifone of the arteries in your body has a diamet~r of 0.0456 centimeter, how many redblood cells could fit across the artery? Write your answer in scientific notation.

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Write"the answer in scientific notation.

9. (6,1 x 105)(2.2 x 106) 10. (2,6 x 10-7)(1.3 x 102) 11. (3.4 X 10-1)(3.1 x 10-2)

12. (5.8 x 10-7)(8.1 x 1012) 13. (4.5 X 104)2 14. (3.7 x 10-5)2

15. (7.2 x 10-3)3 16. 9,9 x 109 17. 8.4 x 10-61.5 X IOs 2.4 X 109

24. (7c7d2)-2 2. (5g4h-3)-3x5y-S

26. --s::6xy

27.16qOr-6 28.

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Write the answer in scientific notation.

9. (2.3 x 10-4)(9.3x 108)

(3.3 x 109)(2.8 x 10-7)

4.62 X 105

10. (5.4 x 10-5)(1.8x 10-1)

(1.2 X 10-4)2

(9.0 x 105)(1.6x 10-8)

11. (2.5 X 10-3)-2

14. 2.1 x 10-48.4 X 10-6

12. 13.

Simplify the expression. Tell which properties of exponents you used.

x2y3 2x4 4m4 3n-115. -. - 16.. -2 y3 -6m-ln5 m-2

(c4)3 12d-6 w-3 v-517 -e 18 -e-. 4 (l5cd)-1 . v-5 w-3

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Write an expression that makes the statement true.

23. a4b-3c5 e ? = a8bclO 24. ? = l:!..- 9x2y6z 3y2

25. (2m3n2)6= ~ e 4m12n-5

26. Chemistry One milliliter of water contains about 3.33 x 1022molecules. About howmany molecules are in a 0.5 liter bottle of water? Write your answer inscientific notation.

27. Manufacturing A package designer for a company that makes holiday ornamentsneeds to decide how to package a special edition glass ornament shaped like asphere. It must be packaged as tightly as possible in a cylinder or a cube.

a. Write an expression for the ratio of the volume of the ornament to the volume ofthe cylinder.

~. Write an expression for the ratio of the volume ofthe ornament to the volume ofthe cube.

c. Which package do you think the designer should choose? Explain.

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Lesson 5. 1Teaching Guide

1. -2: 3 2.81; 9; 729; 729 3.25; 125; 3125;3125 4. It is equivalent to the base raised to thesum of the two exponents. 5. A way to writenumbers using powers of 10 having the formc X Ion where 1::;;c -::::10 and n is an integer;6.4 X 107;3.4 X 10-4

Investigating Algebra Activity

1.8. (6 · 6 . 6 . 6)(6 . 6 . 6 . 6 . 6 . 6 . 6); 611

b. (3 . 3 . 3 . 3 )(3 . 3 . 3 . 3)(3 · 3 · 3 . 3); 312

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4 4 4 4 4 -48 4 8 4 0 4 0 4 45d -e-.-e-e-= . 8-. 7 7 7 7 7 7 8 7 8 7 0 7 8 7' 75

2. See answers to Exercise 1. 3. For the productof powers property, the exponents in theSimplifiedform column are the sum of theexponents in the Exponential expression column.For the power of a power property, the exponentsin the Simplifiedform column are the productof the exponents in the Exponential expressioncolumn. For the quotient of powers property, theexponents in the Simplifiedform column are thedifference of the exponents in the Exponentialexpression column. For the power of a quotientproperty, the exponent in the Exponentialexpression column is applied to the numeratorand denominator to give the expression in theSimplifiedform column. 4. Sample answer:The product.ofpowers property means that if youare multiplying like bases, the exponents will beadded. The power of a power property meansthat if you are raising a power to a power, theexponents will be multiplied. The quotient of apower property means that if you are dividing likebases, the exponents will be subtracted. The powerof a quotient property means that if you areraising a quotient to a power, you will raise boththe numerator and denominator to that power.

Practice Level A1

1.9 2. 125 3.32 4.2565. 1 6.2

7. 19 8. l,oob,ooo 9-20. Check properties.

9.1024 10. -243 11.15,625 12.11 25

13. 32 14.27 15. 1,000,000,000 16. 36

117. -3125 18.8 19.6561 20.32

21.5.27 X 105 22.5.26 X 10-5 23.2.3 X 103

24. 5.983 X 1012 25. 1.76 X 1016

26.7.0 X 10-7 27.4.8 X 109 28.3.534 X 103

29.7.84 X 106 30. 1.849 X 105 31.6.0 X 102

32.7.5 X 101 33-40. Check properties.

33. b6 34. x2 35. sl4 36. 25y2 37. z4

1 x3 16 838. m4 39. 27 40. n2 41.3.26 X 1042. about 2.65 X 104 dollars

Practice Level B

1-8. Checkproperties. 1. 256 2. - 3431 1 1 1 8

3. 16,384 4. 625 5. 256 6.262,144 7. 27

8. li1 9. 1.342X 1012 10.3.38 X 10-5

11. 1.054 X 10-2 12.4.698 X 106

13.2.025 X 109 14. 1.369 X 10-9

15.3.73248 X 10-7 16.6.6 X 101

17.3.5 X 10-15 18-29. Check properties.

18.x4 19.yll 20. 531,441s181 Y 16m7 1

21. 10 22.3 23. ~ 24 ;1w z n 49c d~ 1 #~

25. ~ 26. 2" 27. 4q3r 28 s125g Y 7a

413 _ i 2 - i 4

29. ge5 30. S.- 97TX 31. V - 37TX32

32. V = 37TX6 33. about 1.03 X 1011

34. about 6.1 X 101

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Practice Level C

1-8. Check properties. 1. 25 2. 218764 512

3. 1024 4.256 5. 27 6. 729 7. 19,683

8. 1;5 9.2.139 X 105 10.9.72 X 10-6

11.1.6 X 105 12.2.0 X 10-3 13.1.0 X 10-6

14.2.5 X 101 15-22. Check properties. 15. x62m7 45cl3 9 27r6

16. -6 17. -S 18. 1 19.)42 20.33n d xy qs

21. -h 22. bl8 23. Sample answer: a4b4c5z

24. Sample answer: 6x3y4z 25. Sample answer:

16 6 17 25 2 7Tm n 26. about 1.665 X 10 27.8.3" b."6

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