12. Powers and Exponents Unit Test Review

Math 9

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Write the number of unit squares in this large square as a power.

a. b. 72 c. d. 77

____ 2. Write the base of . a. 5 b. 5 c. d. 3

____ 3. Write as a power. a. c. b. d.

____ 4. Evaluate: a. 30 b. 7776 c. 15 625 d. 11

____ 5. Evaluate: a. 256 b. 16 c. 16 d. 256

____ 6. Evaluate: a. 35 b. 35 c. 78 125 d. 78 125 ____ 7. Evaluate: 107 a. 100 000 000 b. 10 000 000 c. 1 000 000 d. 70 ____ 8. Write one hundred million as a power of 10. a. 1012 b. 108 c. 1011 d. 107

____ 9. Evaluate: a. 8 b. 0 c. 1 d. –1

____ 10. Evaluate: a. 0 b. 1 c. –13 d. –1

____ 11. Evaluate: a. b. 1 c. 1 d. 9

____ 12. Evaluate: a. 1 b. 1 c. d. 30

____ 13. Write in standard form. a. 50 980 b. 50 986 c. 50 981 d. 5986

____ 14. Write the product of as a single power. a. b. c. d.

____ 15. Write the product of as a single power. a. b. c. d.

____ 16. Express as a single power. a. b. c. d.

____ 17. Express as a single power.

a. b. c. d.

____ 18. Evaluate: a. 8 b. 1 c. 1 d. 

Short Answer

19. Write the number of unit cubes in the large cube as a power.

20. Which answers are positive? i) ii) iii) iv)

21. Write 27 and 243 as a power with base 3.

22. Which power is greater, or ? 23. Evaluate:

24. Write in standard form.

25. Write + in standard form.

26. Which number, or 4 400 400, is greater?

27. Write the product of as a single power.

28. Write the product of as a single power.

Challenge Section 29. Evaluate:

30. Simplify, then evaluate.

31. A field measures 105 m by 104 m. a) Write an expression for the area of the field, using powers of 10. b) Write an expression for the perimeter of the field, using powers of 10.

32. Write as a product of powers.

33. Write as a quotient of powers.

34. Evaluate:

35. Simplify, then evaluate.

36. Evaluate: Show your steps.

37. One estimate shows that the number of people without access to safe drinking water is about one billion. How much water is required if each person who does not have access to safe drinking water is given 10 L of safe drinking water? Give your answer in standard form and using powers of 10.

38. Simplify, then evaluate. Show your work.

39. Here are two ways to write 24 as a product of two powers, with at least one of the powers greater than 1.

a) Find two powers that have a product of 48, with at least one power greater than 1. How many different pairs of powers can you find? b) Find two powers that have a product of 96, with at least one power greater than 1. How many different pairs of powers can you find?

40. The scale of a map is 1:100 000. This means 1 cm on the map represents 100 000 cm on land. Determine, in square kilometres, the area represented by an area of 10 cm2 on the map. Explain your thinking.

41. a) Write 128 as a power of 2. b) Write 243 as a power of 3. c) Simplify, then evaluate. Show your work.

42. Simplify, then evaluate. Show your work. Powers and Exponents Unit Test Review Answer Section

MULTIPLE CHOICE

1. ANS: B 2. ANS: A 3. ANS: D 4. ANS: B 5. ANS: A 6. ANS: D 7. ANS: B 8. ANS: B 9. ANS: D 10. ANS: B 11. ANS: C 12. ANS: A 13. ANS: B 14. ANS: A 15. ANS: A 16. ANS: B 17. ANS: C 18. ANS: B

SHORT ANSWER

19. ANS: As a power, the number of unit cubes is . 20. ANS: The answers for i and ii are positive. 21. ANS:

22. ANS: The power is greater. 23. ANS: 24. ANS: 25. ANS:

26. ANS: 4 400 400 is greater. 27. ANS: 28. ANS: 29. ANS: 1458 30. ANS: 31. ANS: a)Area of the field: b) Perimeter of the field:

32. ANS: 33. ANS:

34. ANS:

35. ANS:

PROBLEM 36. ANS:

37. ANS: Each person is to be given 10 L of safe drinking water.

1 billion

The amount of water required is about , or 10 000 000 000 L

38.ANS: 39. ANS:

40. ANS: 1 cm on the map represents 100 000 cm, or 105 cm, on land. 1 m = 100 cm = 102 cm

Convert 105 cm to metres:

1 km = 1000 m = 103 m

Convert 103 m to kilometres:

1 cm on the map represents 1 km on land. 1 cm2 on the map represents 1 km2 on land. So, an area of 10 cm2 on the map represents an area of 10 km2 on land. 41. ANS:

42. ANS: