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Exponents and Scientific Notation

Math 0097  Exponents and Scientific Notation


 

1. Complete the following:

 

2x

x2 x3

x = 3

 

 

 

x = (-3)

 

 

 

x = 4

 

 

 

 

2. Simplify: (0.4)2

 

 

3.  Write 1.65 x 104 in expanded notation:

 

 

4. Write 91.65 in scientific notation:

 

 

5.  Simplify the following expression and leave your answer with positive exponents only:

x-5 x-3 . y-2 y-2

 

 

6.  Divide: x – 3 ) x3 + 0x2 + 0x – 27

 

 

7.  Multiply: x2 · x4

 


8. Simplify: (x5)2

 

 

9. Add the following: 4x + 8x

 

 

10. Simplify: 10x – 12x + 2x

 

 

11.  Simplify: -(3/4)3

 

 

12.  Simplify: (5a2)5 (5a4)3

 

 

 Questions 13-18. Simplify each of the following expressions and leave your answer with positive exponents only:

13. 8z-3

 

 

14. (3a4 b2)2

 

 

15.   b-3 ab-5

 

 

16.   (b-3)-4 (b2)-2 (b-2)-3

 

 

17.   20a5b8 32a7b4

 

 

18.   (20a6b) (30a2b5) 800a4b2

 

 

19. Write 491000000 in scientific notation.

 

 

20. Write 3.24 x 10-6 in expanded notation.

 

 

21. Simplify:  (4 x 10-7) (9 x 1014) 2 x 10-3  Write your answer in scientific notation.

 

 

22. Add:  3x2 – 9x + 11x – 25

 

 

23. Subtract: (3x2 – 5x + 8) – (5x2 – 5x -12)

 

 

Questions 24-27. Multiply each of the following:

24. 3a5 (2a2 + 6a – 7)

 

 

25. (3x + 4) (2x – 5)

 

 

26. (x4 + 8) (x4 – 8)

 

 

27. (3a – 5b)2

 

 

28. Divide 15x3 – 35x2 + 25x by 5x.

 

 

29.   x2 – x – 20 x – 5

 

 

30. Divide:   x3 – 8 x – 2

 

 

31. Simplify:   28x6y6 14x5y10

 

 

32. Subtract 5x – 8 from 9x – 10.

 

 

33. Multiply: (x+8) (x+8)

 

 

34. Multiply: (a2 + 8) (a2 – 8)

 

 

35. Divide:   2x2 – x – 6 x – 2

 

 

 

 

Answers

1.

x

2x

x2

x3

3

6

9

27

(-3)

-6

9

-27

4

8

16

64

2.  0.16

3.  16500

4.  9.165 x 101

5.  1/x2

6.  x2 + 3x + 9

7.  x6

8.  x10

9.  12x

10.  0

11.  –27 64

12.  58a22

13. 8 z3

14.  9a8b4

15. b2 a

16.  b2

17. 5b4 8a2

18. 3a4b4 4

19.  4.91 x 108

20.  0.00000324

21.  1.8 x 1011

22.  3x2 + 2x – 25

23.  -2x2 + 20

24.  6a7 + 18a6 – 21a5

25.  6x2 – 7x -20

26.  x8 – 64

27.  9a2 – 30ab + 25b2

28.  3x2 – 7x + 5

29.  x + 4

30.  x2 + 2x + 4

31. 2x y4

32.  4x – 2

33.  x2 + 16x + 64

34.  a4 – 64

35.  2x + 3