Exponents & Roots – Review Packet – Exercises Hanlonmath.com 1

BASICS OF EXPONENTS

Rewrite, using exponents. 1. 5 x 5 x 5 =____________ 2. 9 x 9 x 9 x 9 x 9 =______________ 3. 6 x 6 = _____________ 4. 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 =________________ 5. 15 x 15 =_______________ 6. 1000 x 1000 x 1000 =_______________ Evaluate. 7. 3 8. 2 9. 5 10. 10 11. 7º 12. 8¹ Rewrite each as a number raised to a power. 13. 27 =____________ 14. 64 =____________ or _____________ 15. 8 =_____________ 16. 144 =_____________ 17. 1000 =______________ 18. 81 = _____________ or _____________

4 3 2

6

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 2

MULTIPLYING AND DIVIDING WITH EXPONENTS

Simplify each. 1. (3²)³ 2. 5² • 5³ 3. 2 • 2 4. (5²) 5. 3 • 3² 6. (4 x 2)² 7. (3²) 8. 2³ x 2 9. (4 x 4)² 10. (3n)³ 11. 10 x 10 12. (4a²)² 13. (3c³) 14. 5 x 5² 15. (4²)² 16. (5 x 3)² 17. (6a )2 18. 9² x 9² 19. (9²)² 20. (6 )³ Write in simplest form.

.22 ³־3 .212

355 23.

234

⎛ ⎞⎜ ⎟⎝ ⎠

4 5

4 4

4 4

4 5

4 4

5

4

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 3

24. 7n25 ²־. (7n)26 ²־. 34

5⎛ ⎞⎜ ⎟⎝ ⎠

27. 5

344 28. (2n) -­‐3 29.

5

377

30.

2 2

4( )nn

31. 3

4(2 )aa 32. (3a³) -2

33. 4a -3 34. (n²) -3 35. (2²) -3

36. 31

3⎛ ⎞⎜ ⎟⎝ ⎠

37. 3a38 �־. (3a)־�

39. 4 -2 40. 5 -3

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 4

SIMPLIFYING SQUARE ROOTS

Find the square root of each. 1. 25 2. 49 3. 100 4. 81 5. 121 6. 400 7. 256 8. 1 9. 169 10. 9 Simplify. 11. 32 12. 500 13. 75 14. 45 15. 12 16. 99 17. 80 18. 175 19. 108

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 5

20. 44 21. 128 22. 112 23. 117 24. 125 25. 63

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 6

APPROXIMATING SQUARE ROOTS

Determine which two consecutive whole numbers each radical’s value is between. 1. _______ < 7 < _______ 2. ________< 24 < ________ 3. _______< 92 < ________ 4. ________< 45 < ________ 5. _______< 53< _________ 6. ________< 150 < ______ 7. ______< 18 < ________ 8. ________< 71 < ________ 9. _______ < 28 < _________ 10. _______ < 140 < _____ 11. _______ < 29 < _________ 12. _______< 66 < ________ 13. _______< 3 < __________ 14. _______ < 15 < _______ 15. _______< 85 < ________

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 7

ADDING AND SUBTRACTING SQUARE ROOTS

Simplify. 1. 4 7 + 5 7 2. 9 3 – 3 3 3. 9 – 25 4. 6 8 + 3 2 5. 4 8 – 32 6. 25 + 2 25 7. 3 72 – 5 2 8. 3 24 + 5 54 9. 8 + 3 50 10. 7 7 – 63 11. 25 + 81 12. 147 – 75

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 8

13. 2 5 + 45 14. 49 + 64 15. 2 28 – 2 7 16. 3 20 – 4 45

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 9

MULTIPLYING AND DIVIDING SQUARE ROOTS

Simplify. 1. 3 x 7 2. 5 x 11 3. 8 x 2 4. 3 2 x 2 6 5. 3 5 x 4 10 6. 3 x 4 15 7. 18 x 8 8. 4 14 x 7 9. 63 x 7 10. 2 5 x 3 10 11. 24 x 56 12. 7 x 2 21 13. 17 x 34 14. 3 3 x 7 7

15. 10 x 20 16. 35

17. 4 32 6

18. 6 25

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 10

19. 812

20. 14168 7

21. 144

8 22. 20

40

23. 21 217 3

24. 248

25. 73

26. 36

27. 9 264 2

28. 633 7

29. 208

30. 3 35 6

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 11

SCIENTIFIC NOTATION

Convert to scientific notation. 1. 3,420,000 = ___________________ 2. 72,000,000,000 = ____________________ 3. 8,450 = __________________ 4. 930,000 = ___________________ 5. 5,000 = ____________________ 6. 43,600,000,000,000 = ______________________ 7. 7,023,000 = _____________________ 8. 2,150 = __________________ 9. 999,000,000 = _____________________ 10. 61,000 = ___________________ 11. 0.0000724 = _____________________ 12. 0.00903 = __________________ 13. 0.04 = ______________________ 14. 0.000000000022 = _____________________ 15. 0.00000008 = ___________________ 16. 0.0000601 = ___________________ 17. 0.00000001 = ____________________ 18. 0.0035 = ____________________

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 12

19. 0.000000123 = ___________________ 20. 0.0000005 = ___________________ Convert to standard form. 21. 4.32 x 10 = ___________________ 22. 3.09 10 = ___________________ 23. 1.17 x 10 = ___________________ 24. 2.7 x 10 = __________________ 25. 1 x 10 8 = ________________ 26. 3.115 x 10 = _________________ 27. 4.3 x 10³ = ________________ 28. 8.11 x 10 = _________________ 29. 5.68 x 10 = ______________ 30. 8.9 x 10 2 = _____________ 31. 4.32 x 10 -3 = _____________ 32. 8.45 x 10 -7 = ____________ 33. 4.01 x 10 -4 = _______________ 34. 3.9 x 10 -8 = ____________ 35. 5.621 x 10 -8 = _____________ 36. 7.69 x 10 -6 = _____________

7 4 11 5 6 9 10

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 13

37. 9.1 x 10 -5 = ____________ 38. 1.005 x 10 -9 = ____________ 39. 5.14 x 10 -2 = ____________ 40. 2 x 10 ˉ¹¹ = ______________

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 14

CUMULATIVE REVIEW

Rewrite using exponents. 1. 4 x 4 x 4 = _____________ 2. 2 x 2 x 2 x 2 x 2 x 2 x 2 = ______________ 3. 8 x 8 x 8 x 8 x 8 = ________________ 4. 24 x 24 x 24 x 24 = _________________ Evaluate. 5. 3 6. 2 7. 14º 8. 8¹ Simplify. Make all exponents positive 11. (2x³) 12. (4a³) -2 13. (4a -2 ) 2 14. (a 4 ) -3

15. 7

555−

16. 32

3⎛ ⎞⎜ ⎟⎝ ⎠

17 2 2

5(4 )aa

18. (3x)ˉ³ Simplify. 19. 3 3 + 7 3 20. 4 5 + 20

4 7 4

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 15

21. 8 3 – 12 22. 8 3 – 3 3 23. 3 2 x 4 5 24. 14 x 7

25. 27 x 3 3 26. 4 721

27. 63

28. 5 119 22

Convert to scientific notation.

29. 8,470,000 = ___________________

30. 0.00000775 = ________________________

31. 7,450 = ______________________

32. 0.009 = ______________________

33. 89,700,000,000 = ________________________

34. 0.0094576 = ____________________

Convert to standard form.

35. 8.29 x 10 7 = ____________________ 36. 1.33 x 10 -5 = _____________________ 37. 2.0173 x 10 = _____________________ 38. 7.014 x 10 = _____________________ 39. 5.1 x 10 -10 = _______________________ 40. 8.3 x 10 -5 = ______________________

6 8־

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 16

Between which two consecutive whole numbers is each other between? 41. ___________< 19 < _____________ 42. ___________ < 75 < _____________ 43. ___________ < 50 < _____________ 44. ___________ < 110 < _____________

Exponents & Roots – Review Packet – Exercises Hanlonmath.com 17

1.) Which would not give you the same answer as (3²)³? A. 27² B. 3 5 C. 3 6 D. 9³ E. All give you the correct answer 2.) 8.384 x 10³ = ? A. 0.00834 B. 0.0834 C. 838.4 D. 8384 E. 83,840 3.) 225 is the same as which expression below? A. 5³ x 2 B. 5² x 3² C. 5 x 3 D. 225 x 10² E. 25 x 5² 4.) The “cube root of 125” is written as: A. 125² B. 125³ C. 12 -3 D. 1252 E. 1253 5. Simplify: 96 A. 2 48

B. 6 4

C. 6 16

D. 4 6

E. 16 6