Free Printable Exponents and Operations of Scientific Notation

1.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

2.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

3.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

4.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

5.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

6.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

7.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

8.

How do you write 2 x 2 x 2 x 2 with an exponent?

a)

4²

b)

2⁴

c)

2²

9.

Simplify (2⁴)(2⁵)

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

10.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

11.

Write $\left(\frac{2}{5}\right)^4$ as repeated multiplication.

a)

$\left(\frac{2}{5}\right)\left(\frac{3}{5}\right)\left(\frac{2}{5}\right)\left(\frac{3}{5}\right)$

b)

$\left(\frac{2}{3}\right)\left(\frac{2}{5}\right)\left(\frac{2}{3}\right)\left(\frac{2}{5}\right)$

c)

$\left(\frac{2}{3}\right)\left(\frac{2}{3}\right)\left(\frac{2}{3}\right)\left(\frac{2}{3}\right)$

d)

$\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)$

12.

m ⋅ m⁵⋅ m⁶

a)

m³⁰

b)

m¹²

c)

12m

d)

mm¹¹

13.

(8⁵)³

a)

8⁸

b)

8²

c)

8¹⁵

d)

1/8²

14.

3x⁴ * 6x⁶

a)

18x¹⁰

b)

18x²⁴

c)

9x¹⁰

d)

9x²⁴

15.

Simplify the expression

8^{-23}

a)

$8^{23}$

b)

$\frac{1}{8^{-23}}$

c)

$\frac{1}{23}$

d)

$\frac{1}{8^{23}}$

16.

(4x³)²

a)

8x⁵

b)

8x⁶

c)

16x⁵

d)

16x⁶

17.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

18.

Which expression is equivalent (equal) to ( n * y)⁶

a)

6n * 6y

b)

n⁶ * y⁶

c)

n⁶y⁶

19.

Which expression is equivalent (equal) to

a)

10^-12

b)

10^-6

c)

1/10⁶

d)

1/10¹²

20.

Which expression is equivalent (equal) to

a)

6³

b)

6⁴

c)

6²

d)

6⁶

21.

Which expression is equivalent (equal) to

a)

6³

b)

6⁴

c)

6²

d)

6⁶

22.

(8⁵)³

a)

8⁸

b)

8²

c)

8¹⁵

d)

1/8²

23.

3x⁴ * 6x⁶

a)

18x¹⁰

b)

18x²⁴

c)

9x¹⁰

d)

9x²⁴

24.

(4x³)²

a)

8x⁵

b)

8x⁶

c)

16x⁵

d)

16x⁶

25.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

26.

Simplify. Your answer should contain only positive exponents

$2m^2\cdot3m^4$

a)

$6m^6$

b)

$6m^8$

c)

$5m^6$

d)

$5m^8$

27.

$4^5\ \times4^4$

a)

$4^9$

b)

$16^9$

c)

$8^9$

d)

$4^1$

28.

$6^2\ \times6^4$

a)

$36^6$

b)

$12^6$

c)

$6^6$

d)

$6^8$

29.

$12^{3\ }\times12^4$

a)

$144^7$

b)

$12^7$

c)

$12^{12}$

d)

$144^{12}$

30.

$4^{7\ }\times4^5$

a)

$4^{35}$

b)

$16^7$

c)

$16^{35}$

d)

$4^{12}$

31.

$8^{8\ }\times\ 8^2$

a)

$8^{16}$

b)

$8^{10}$

c)

$64^{10}$

d)

$64^{64}$

32.

$\left(4^3\right)^2$

a)

$4^5$

b)

$4^1$

c)

$4^6$

d)

$4^{32}$

33.

$\left(5^4\right)^2$

a)

$5^8$

b)

$5^6$

c)

$5^2$

d)

$20^2$

34.

$\left(7^5\right)^3$

a)

$7^2$

b)

$7^{15}$

c)

$35^3$

d)

$7^8$

35.

$\left(12^6\right)^3$

a)

$12^9$

b)

$12^3$

c)

$72^3$

d)

$12^{18}$

36.

$\left(2^7\right)^2$

a)

$2^{14}$

b)

$14^2$

c)

$2^5$

d)

$14^{14}$

37.

Change from standard form to scientific notation: 12,000,000

a)

12.0 x 10⁷

b)

0.12 x 10⁷

c)

1.2 x 10⁶

d)

1.2 x 10⁷

38.

Change from standard form to scientific notation: 450,000

a)

4.5 x 10⁵

b)

45 x 10⁵

c)

4.5 x 10⁴

d)

4.5 x 10⁶

39.

Change from standard form to scientific notation: 0.000398

a)

39.8 x 10^-5

b)

3.98 x 10^-5

c)

3.98 x 10^-4

d)

39.8 x 10^-6

40.

Change from standard form to scientific notation: 0.004078

a)

4.078 x 10^-3

b)

4.078 x 10³

c)

40.78 x 10^-4

d)

.4078 x 10^-2

41.

Which number is correctly written in scientific notation?

a)

5.67 x 10⁵

b)

56.7 x 10³

c)

0.567 x 10⁶

42.

Which number is correctly written in scientific notation?

a)

8.2 x 10²

b)

82 x 10⁷

c)

3.45 x 9⁴

43.

How would you write 0.0005 in scientific notation?

a)

50 x 10⁵

b)

5 x 10⁴

c)

5 x 10³

d)

.5 x 10³

44.

How would you write -5.6 x 10^-3 in standard form?

a)

0.0056

b)

-5,600

c)

0.00056

d)

-0.0056

45.

The rule of scientific notation is to write all exponents with a base of ____.

a)

50

b)

5

c)

100

d)

10

46.

Which of the following in the LARGEST number?

a)

9 x 10⁶

b)

8 x 10¹⁰

c)

1.3 x 10¹²

d)

5.3 x 10³

47.

Which one of these is in scientific notation?

a)

8.987000

b)

8.98 x 10⁶

c)

80.987 x 10

d)

8.98⁶

48.

Write 9.8 x 10^-5in standard form

a)

0.00098

b)

0.000098

c)

.098

d)

98,000

49.

Which is the correct coefficient of 23,400,000 when it is written in scientific notation?

a)

0.234

b)

2.34

c)

234.

d)

23.4

50.

125,678,000: Change to scientific notation

a)

1.25678 x 10¹²

b)

.125678 x 10^-9

c)

12.5678 x 10⁸

d)

1.25678 x 10⁸

51.

Try to change the number back to standard form: 6.79 x 10⁴

a)

679,000

b)

6,790

c)

67,900

d)

6,790,000

52.

Try to change the number back to standard form: 3.97 x 10^-2

a)

0.000397

b)

0.0397

c)

0.0000397

d)

0.397

53.

Write 2.08 x 10²in standard form.

a)

208

b)

0.0208

c)

20,800

d)

0.208

54.

How do you write
1001
in scientific notation?

a)

1.0001 x 10⁴

b)

1.01 x 10⁵

c)

1.001 x 10³

d)

10.1 x 10³

55.

Change from standard form to scientific notation: 12,000,000

a)

12.0 x 10⁷

b)

0.12 x 10⁷

c)

1.2 x 10⁶

d)

1.2 x 10⁷

56.

Change from standard form to scientific notation: 450,000

a)

4.5 x 10⁵

b)

45 x 10⁵

c)

4.5 x 10⁴

d)

4.5 x 10⁶

57.

Change from standard form to scientific notation: 0.000398

a)

39.8 x 10^-5

b)

3.98 x 10^-5

c)

3.98 x 10^-4

d)

39.8 x 10^-6

58.

Change from standard form to scientific notation: 0.004078

a)

4.078 x 10^-3

b)

4.078 x 10³

c)

40.78 x 10^-4

d)

.4078 x 10^-2

59.

125,678,000: Change to scientific notation

a)

1.25678 x 10¹²

b)

.125678 x 10^-9

c)

12.5678 x 10⁸

d)

1.25678 x 10⁸

60.

Which number is correctly written in scientific notation?

a)

5.67 x 10⁵

b)

56.7 x 10³

c)

0.567 x 10⁶

61.

Which number is correctly written in scientific notation?

a)

8.2 x 10²

b)

82 x 10⁷

c)

3.45 x 9⁴

62.

7.82 x 10^-⁶ is an example of scientific notation. The exponent of -6 tells you your number will be very ________.

a)

Large

b)

Small

c)

Basic

63.

The factor multiplied by a power of 10 in scientific notation needs to be greater than or equal to one but less than ___________?

a)

1

b)

10

c)

100

d)

1,000

64.

How would you write 0.0005 in scientific notation?

a)

50 x 10⁵

b)

5 x 10⁴

c)

5 x 10³

d)

.5 x 10³

65.

The rule of scientific notation is to write all exponents with a base of ____.

a)

50

b)

5

c)

100

d)

10

66.

Which of the following in the LARGEST number?

a)

9 x 10⁶

b)

8 x 10¹⁰

c)

1.3 x 10¹²

d)

5.3 x 10³

67.

Which of the following numbers is the SMALLEST?

a)

8.7 x 10³

b)

3 x 10⁴

c)

1.3 x 10⁸

d)

9 x 10²

68.

Write 2.08 x 10²in standard form.

a)

208

b)

0.0208

c)

20,800

d)

0.208

69.

Write 3.2 x 10³in standard form.

a)

3.200

b)

3200

c)

32000

d)

.0032

70.

Light travels at a rate of 186,000 miles per second. Write this number in scientific notation.

a)

1.86 x 10⁵

b)

1.86 x 10⁴

c)

18.6 x 10⁴

d)

186 x 10³

71.

The closest galaxy to our own is over 2,500,000 light years away. Write this number is scientific notation.

a)

2.5 x 10⁷

b)

.25 x 10⁷

c)

25 x 10⁵

d)

2.5 x 10⁶

72.

If the exponent is a positive number the original number was...

a)

a really big number.

b)

a really small number.

73.

If the exponent is a negative number the original number was...

a)

a really large number.

b)

a really small number.

74.

Which is the correct coefficient of 23,400,000 when it is written in scientific notation?

a)

0.234

b)

2.34

c)

234.

d)

23.4

75.

The mass of a substance is 8 X 10⁹ micrograms. If one microgram is equal to 1 X 10^-6 grams, what is its mass in grams?

a)

1.25 X 10^-15 grams

b)

1.25 X 10^-3 grams

c)

8 X 10³ grams

d)

8 X 10¹⁵ grams

76.

Multiply:
(3.4 x 10⁵)(1.2 x 10^-3)

a)

4.08 x 10^-8

b)

4.8 x 10²

c)

4.08 x 10²

d)

4.08 x 10^-15

77.

Write the answer in scientific notation.

4.1 x 10⁵ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁵

c)

9.6 x 10¹¹

d)

4.65 x 10⁵

78.

Find the difference.

(3.8 x 10⁴) - (2 x 10³)

a)

1.8 x 10⁴

b)

1.8 x 10¹

c)

3.6 x 10¹

d)

3.6 x 10⁴

79.

Divide:
5.2 x 10¹¹ ÷ 2 x 10⁵

a)

3.2 x 10⁶

b)

2.6 x 10⁶

c)

2.6 x 10¹⁶

80.

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

a)

30.08 x 10¹¹

b)

3.8 x 10¹

c)

3.008 x 10¹²

d)

2.9375 x 10¹

81.

(5x10¹⁰) x (3x10⁷)

a)

15x10¹⁷

b)

1.5x10¹⁷

c)

1.5x10¹⁸

d)

1.5x9¹⁷

82.

Solve:
(2.1×10²) × (3.0×10⁴)

a)

5.1 x 10²

b)

6.3 x 10⁶

c)

5.1 x 10⁶

d)

6.3 x 10⁸

83.

What is the simplified version of

a)

3.9 x 10⁶

b)

4 x 10²⁰

c)

4 x 10⁶

d)

3.9 x 10²⁰

84.

Subtract the within the scientific notation.
(2 x 10³) - (1.9 x 10²)

a)

1.81 x 10⁵

b)

1.81 x 10³

c)

1.81 x 10⁶

d)

1.81 x 10⁴

85.

(2.3 x 10²)+(4.1 x 10²)=

a)

6.4 x 10⁴

b)

6.4 x 10²

c)

6.4 x 10⁰

d)

.64 x 10¹

86.

Write the answer in scientific notation.
4.1 x 10⁵ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁵

c)

9.6 x 10¹¹

d)

4.65 x 10⁵

87.

Write the answer in scientific notation.
5 x 10⁸ - 3.4 x 10⁸ =

a)

2.4 x 10⁸

b)

2.4 x 10⁰

c)

1.6 x 10⁰

d)

1.6 x 10⁸

88.

Give the sum of (9.54 x 10⁸) + (3.22 x10⁷) in scientific notation

a)

1.276 x 10⁷

b)

8.62 x 10¹⁵

c)

12.76 x 10⁸

d)

9.862 x 10⁸

89.

Give the sum of (8.7 x 10^-7) + (3.23 x 10^-5)

a)

1.193 x 10^-12

b)

3.317 x 10^-5

c)

3.317 x 10^-12

d)

5.53 x 10^-2

90.

Give the difference of (6.4 x 10^-6) - (5.7 x 10^-7)

a)

5.83 x 10^-6

b)

7 x 10^-7

c)

1.23 x 10^-13

d)

1.3 x 10^-6

91.

Multiply:
(3.4 x 10⁵)(1.2 x 10^-3)

a)

4.08 x 10^-8

b)

4.8 x 10²

c)

4.08 x 10²

d)

4.08 x 10^-15

92.

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

a)

3 x 10¹⁰

b)

3 x 10⁴

c)

3 x 10^-4

d)

3 x 10^-11

93.

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

a)

30.08 x 10¹¹

b)

3.8 x 10¹

c)

3.008 x 10¹²

d)

2.9375 x 10¹

94.

Solve:
(2.1×10²) × (3.0×10⁴)

a)

5.1 x 10²

b)

6.3 x 10⁶

c)

5.1 x 10⁶

d)

6.3 x 10⁸

95.

Solve:
(6 x 10⁶) / (2 x 10³)

a)

12 x 10³

b)

3 x 10⁹

c)

1.2 x 10⁴

d)

3 x 10³

96.

Write the answer in scientific notation.
7.3 x 10⁵ + 3.7 x 10⁵ =

a)

11.0 x 10⁵

b)

1.1 x 10¹⁰

c)

1.10 x 10¹¹

d)

1.1 x 10 ⁶

97.

Write the answer in scientific notation.
4.1 x 10⁵ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁵

c)

9.6 x 10¹¹

d)

4.65 x 10⁵

98.

What is the simplified version of

a)

3.9 x 10⁶

b)

4 x 10²⁰

c)

4 x 10⁶

d)

3.9 x 10²⁰

99.

(7.7 x 10²) + (1.1 x 10²)=

a)

8.8 x 10⁴

b)

6.6 x 10⁴

c)

8.8 x 10²

d)

6.6 x 10²

100.

Which is the smallest?
1.3 x 10²⁰2.9 x 10²¹9.5 x 10³²8.4 x 10¹⁹

a)

1.3 x 10²⁰

b)

2.9 x 10²¹

c)

9.5 x 10³²

d)

8.4 x 10¹⁹

101.

Which is the largest?
4.8 x 10^-6
1.3 x 10²⁰3.1 x 10^-49.2 x 10^-59.5 x 10³²5.9 x 10^-52.9 x 10²¹8.4 x 10¹⁹

a)

9.5 x 10³²

b)

3.1 x 10^-4

c)

8.4 x 10¹⁹

d)

4.8 x 10^-6

102.

(2.9 x 10^-9) - (1.7 x 10^-9)

a)

1.2 x 10^-18

b)

1.2 x 10^-9

c)

4.6 x 10^-9

d)

1.335 x 10^-4

103.

How would you write 564,000,000 in scientific notation?

a)

5.64 x 10^-7

b)

5.64 x 10⁶

c)

5.64 x 10⁸

d)

56.4 x 10⁷

104.

Which of the following is correct scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

105.

Write the answer in scientific notation.
7.3 x 10⁵ + 3.7 x 10⁵ =

a)

11.0 x 10⁵

b)

1.1 x 10¹⁰

c)

1.10 x 10¹¹

d)

1.1 x 10 ⁶

Exponents and Operations of Scientific Notation

Total questions: 105

Worksheet time: 9hrs 45mins

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