Free Printable Power rules and and Scientific Notation practice

1.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

2.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

3.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

4.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

5.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

6.

3³ ⋅ 3

a)

3⁴

b)

3³

c)

3⁰

d)

1 ⁄ 3⁴

7.

Simplify
x⁰

a)

x

b)

⁰

c)

1

d)

Undefined

8.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

9.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

10.

Simplify the expression.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

11.

6k²⋅ k

a)

6

b)

6k

c)

6k²

d)

6k³

12.

(g⁵)⁸

a)

g¹³

b)

5g⁸

c)

g⁴⁰

d)

8g⁵

13.

4²* 4²

a)

16⁴

b)

4²

c)

4⁴

d)

8²

14.

2 * 2² *2²

a)

2⁴

b)

8⁴

c)

36

d)

2⁵

15.

3²*3²

a)

3⁴

b)

9⁴

c)

9²

d)

3²

16.

a)

1¹⁰

b)

1²⁶

c)

z¹⁰

d)

z²⁶

17.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

18.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

This cannot be determined.

19.

Simplify (-4x)⁰

a)

-4

b)

-4x

c)

-1

d)

1

e)

0

20.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

21.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

22.

z⁰

a)

z

b)

0

c)

1

23.

Simplify

w⁵(w^x)w⁷

a)

w^35x

b)

w¹³

c)

w^12x

d)

w^{12 + x}

24.

2⁰x⁰y⁰ = ?

a)

2⁰x⁰y⁰ = 0

b)

2⁰x⁰y⁰ = 1

c)

2⁰x⁰y⁰ = 2xy

d)

2⁰x⁰y⁰ = 2

25.

7x⁰

a)

7x

b)

7

c)

1

d)

0

26.

Simplify (-9)⁰

a)

-9

b)

-1

c)

1

d)

9

27.

$m^3n^0=$

a)

1

b)

$n^{30}$

c)

$m^3$

d)

0

28.

$x^2y^0=$ Hint: the zero exponent is only applied to the letter y.

a)

1

b)

$x^2$

c)

0

d)

z

29.

$5^0\ =\$

a)

1

b)

5

c)

50

d)

0

30.

$7^0\ =\$

a)

7

b)

0

c)

70

d)

1

31.

$x^0\ =\$

a)

1

b)

y

c)

x

d)

0

32.

$m^0\ =\$

a)

10

b)

m

c)

1

d)

0

33.

Any expression raised to the zero power is...?

a)

0

b)

1

c)

2

d)

negative

34.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

35.

Simplify the following expression:

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

36.

Simplify the following expression:

2x³y⁵ ⋅ 5xy²

a)

10x⁴y⁷

b)

7x⁴y⁷

c)

10x³y¹⁰

d)

7x³y¹⁰

37.

Simplify the following expression:

r⁶⋅ r²⋅ r³

a)

r⁶²³

b)

r¹¹

c)

11r

d)

r³⁶

38.

If the bases are the same, then you....

a)

Multiply the exponents

b)

Subtract the exponents

c)

Add the exponents

d)

Divide the exponents

39.

x^{20 .} x¹⁰

a)

x³⁰

b)

x²⁰⁰

c)

2x³⁰

d)

x¹⁰

40.

5², in this example, 5 is the ______ and 2 is the _______

a)

base, product

b)

exponent, base

c)

base, exponent

d)

product, base

41.

Which number is the EXPONENT?

4^{2 =}16

a)

4

b)

16

c)

2

d)

162

42.

Which number is the BASE?

2³= 8

a)

2

b)

8

c)

3

d)

238

43.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

44.

Simplify the expression.
(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

45.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

46.

Simplify

-10k² ∗ k

a)

-10k³

b)

-10k²

c)

-9k³

d)

-9k²

47.

Simplify

4 ∗ x

a)

4x

b)

4x²

c)

x²

d)

4

48.

Simplify

(9h)(-4h)

a)

-36h²

b)

-36h

c)

5h

d)

5h²

49.

Simplify

-4m² ∗ m²

a)

-4m⁴

b)

-3m⁴

c)

-3m²

50.

Simplify

x ∗ x

a)

x²

b)

2x

c)

2x²

d)

x

51.

Simplify

2x³ ∗ 4x⁵

a)

8x⁸

b)

6x⁸

c)

6x¹⁵

d)

8x¹⁵

52.

Simplify

(v⁵)(v⁵)

a)

v¹⁰

b)

v²⁵

c)

2v¹⁰

d)

2v²⁵

53.

Simplify

c¹² ∗ c¹³

a)

c²⁵

b)

c¹⁵⁶

c)

c¹²³

d)

2c²⁵

54.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

55.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

56.

5³⋅5⁴

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

57.

6⋅6⁷

a)

6⁸

b)

6⁶

c)

6⁷

d)

6

58.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

59.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

60.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

61.

3⁻⁴

a)

1 ⁄ 3⁴

b)

-3⁴

c)

3⁴

d)

1 ⁄ 12

62.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

63.

(3y⁴)²

a)

9y⁸

b)

9y⁶

c)

6y⁸

d)

6y⁶

64.

Fill in the blank with the correct exponent to make the statement true.
3^{16 =}(3⁸)(3^_)

a)

2

b)

8

c)

4

d)

1

65.

Evaluate the expression using the quotient rule.

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

66.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

67.

(7uv²)^-5

a)

-35uv^-10

b)

-5/7uv²

c)

1/7⁵u⁵v¹⁰

d)

1/7uv¹⁰

68.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

69.

(ab⁸c)(a^-17c¹⁰)

a)

a¹⁷b⁸c¹¹

b)

a¹⁶b⁸c¹¹

c)

(b⁸c¹¹)/(a¹⁶)

d)

a^-17b⁸c¹⁰

70.

Simplify (7a²)(5a⁶b)²

a)

35a¹⁴b²

b)

175a¹²b²

c)

175a¹⁴b²

d)

35a¹⁴b

71.

Simplify (7a²)(5a⁶b)²

a)

35a¹⁴b²

b)

175a¹²b²

c)

175a¹⁴b²

d)

35a¹⁴b

72.

(x⁸)(x^-5)

a)

x^-40

b)

x^-13

c)

x¹³

d)

x³

73.

(t^-6)^-5

a)

t^-11

b)

t^-30

c)

t³⁰

d)

t¹¹

74.

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

a)

add

b)

subtract

c)

multiply

d)

divide

75.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

76.

Simplify
(-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

77.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

78.

a)

9^-4

b)

9^-45

c)

3^-4

d)

3^-45

79.

a)

6^-2

b)

1/6²

c)

1/36

d)

All of the above

80.

a)

4⁹

b)

4⁴⁴

c)

4²¹

d)

4¹⁵

81.

a)

0

b)

3

c)

1

d)

-1

82.

Simplify the surds then complete the subtration: 8√84 - 5√84

a)

3√84

b)

2√21

c)

6√21

d)

5√10

83.

Simplify

a)

13√3

b)

10√30

c)

13√6

d)

11√3

84.

Simplify 3√48 - √75

a)

17√3

b)

48

c)

7√3

d)

48√3

85.

Simplify the expression $5^{-8}$

a)

$5^8$

b)

$\frac{1}{5^8}$

c)

$\frac{1}{-5^{-8}}$

d)

$\frac{1}{5^{-8}}$

86.

Rewrite using a positive exponent.

$2w^{-13}$

a)

$-w^{13}$

b)

$\frac{2}{w^{13}}$

c)

$\frac{2}{w^{-13}}$

d)

$2w^{13}$

87.

Select ALL that are correct.

Simplify the following: $\left(2x^4y^{-3}\right)^{-1}$

a)

$2^{-1}x^{-4}y^3$

b)

$-\frac{2}{x^4y^3}$

c)

$\frac{1}{2x^4y^3}$

d)

$\frac{y^3}{2x^4}$

88.

a)

b)

c)

d)

89.

Simplify the expression: $\frac{5^8}{5^{-4}}$

a)

5^-32

b)

5^-4

c)

5⁴

d)

5¹²

90.

a)

b)

c)

d)

91.

a)

b)

c)

d)

92.

Which of the following show what should be done with the exponents to simplify: $\frac{5^{-4}}{5^3}$

a)

$-4+3$

b)

$-4\left(3\right)$

c)

$4+3$

d)

$-4-3$

93.

Simplify: $\frac{8^{-9}}{8^2}$

a)

$8^{-7}$

b)

$8^{18}$

c)

$8^{-11}$

d)

$8^{-9}$

94.

Simplify: $\frac{3^{-7}}{3^{-2}}$

a)

$3^5\$

b)

$3^{-9\ }=\frac{1}{3^9}$

c)

$3^{-5}\ =\frac{1}{3^5}$

d)

$3^9$

95.

Simplify: $\frac{3^0}{3^{-6}}$

a)

$3^{-6}$

b)

$3^6$

c)

$18$

d)

$9$

96.

Evaluate the expression using the quotient of powers rule.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

a⁸b⁷

97.

$\frac{18x^{10}}{2x^3}$

a)

$9x^7$

b)

$9x^{13}$

c)

$18x^7$

d)

$2x^{13}$

98.

Simplify $\frac{a^3b}{a^6b^2}$ .

a)

$\frac{1}{a^3b}$

b)

$a^3b$

c)

$a^9b^3$

d)

$\frac{1}{a^9b^3}$

99.

Can $\frac{b^5}{b^2}$ be simplified?

a)

Yes.

b)

No.

c)

I don't know, ask my teacher.

100.

Simplify $\frac{x^3}{x^5}$ .

a)

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

b)

$x^2$

c)

$\frac{1}{x^2}$

d)

$x^8$

101.

The half-life of Uranium is 2.5 x 10⁵ years. What is this in standard form?

a)

2500000

b)

250

c)

25000

d)

250000

102.

Write 4.83 x 10^-6in Standard Form.

a)

0.00048300

b)

0.00004830

c)

0.00000483

d)

0.00000438

103.

Convert 0.0000037 to Scientific Notation.

a)

.37 x 10^-7

b)

3.7 x 10^-6

c)

37 x 10^-5

d)

370 x 10^-4

104.

Mercury’s average distance from the sun is 57,190,000 km. What is the distance in scientific notation?

a)

5719 x 10⁴

b)

571.9 x 10⁵

c)

57.19 x 10⁶

d)

5.719 x 10⁷

105.

(3 x 10⁷)(3.1 x 10^-4)

a)

9.3 x 10^-28

b)

9.3 x 10³

c)

6.1 x 10³

d)

6.1 x 10^-28

106.

a)

2.1 x 10⁶

b)

2.1 x 10^-6

c)

9.9 x 10⁶

d)

9.9 x 10^-6

107.

The thickness of a human hair can be about 6 x 10^-3 centimeters. Which shows this thickness in standard form?

a)

6000 cm

b)

0.06 cm

c)

0.006 cm

d)

0.0006 cm

108.

The speed of light is about 300 million meters per second. Which expression shows this speed in scientific notation?

a)

300 x 10⁶

b)

300 x 10^-6

c)

3 x 10⁸

d)

3 x 10^-8

109.

To travel from Earth to Saturn, the craft needs to travel a total distance of 1.4 x 10⁹ km. A spacecraft leaves Earth’s orbit at a speed of 7 x 10⁵ km per day. How long will it take the spacecraft to reach Saturn? Express your answer in correct scientific notation.

a)

2 x 10⁴

b)

0.2 x 10⁴

c)

2 x 10³

d)

0.7 x 10⁴

110.

There are approximately 3.1 x 10⁸ people in the United States. If on average each person has 4.1 x 10¹ coins lying around on dressers, in pockets, in cars, etc., how many total coins do all the people in the U.S. have?

a)

127.1 x 10⁸

b)

12.71 x 10⁹

c)

1.271 x 10¹⁰

d)

.1271 x 10¹¹

111.

There are approximately 3.61 x10⁵babies born every day. How many babies are born in 30 days? Choose all that are correct.

a)

10830000

b)

10.83 x 10⁶

c)

1.083 x 10⁷

d)

.1083 x 10⁸

112.

The average distance from Jupiter to the Sun is about 5 x 10⁸ miles. The average distance from Venus to the Sun is about 7 x 10⁷ miles. Which planet is further from the Sun?

a)

Venus

b)

Earth

c)

Mars

d)

Jupiter

e)

Saturn

113.

How would you write 4.3756 x 10⁴in standard form?

(a)

114.

How would you write 0.0005 in scientific notation?

a)

50 x 10^-5

b)

5 x 10^-4

c)

5 x 10³

d)

.5 x 10³

115.

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

(a)

116.

Scientific Notation is made up of two number parts. The first part should be a number between 1 and 100.

a)

True

b)

False

117.

Scientific Notation is made up of two number parts. The second part is a power 10.

a)

True

b)

False

118.

How do you write 8.317 x 10⁶in standard form?

(a)

119.

Which of the following numbers is written in scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

120.

Express the following in scientific notation:

.000457

a)

457 x 10⁶

b)

457 x 10^-6

c)

4.57 x10⁴

d)

4.57 x 10^-4

121.

Convert to scientific notation:

520,000,000

a)

52 x 10⁷

b)

5.2 x 10^-7

c)

5.2 x 10⁸

d)

0.52 x 10⁹

122.

What is scientific notation?

a)

A long way to write really short numbers

b)

A short way to write really large or really small numbers

c)

I don't know...

d)

None of the above

123.

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

a)

a really big number.

b)

a really small number.

124.

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

a)

a really large number.

b)

a really small number.

125.

Convert this number to standard notation:

7.1 x 10⁴

(a)

126.

Convert this number into scientific notation:

0.068

a)

6.9 x 10⁶

b)

6.8 x 10^-9

c)

6.8 x 10^-2

d)

None of the above

127.

Convert this number to standard notation:

1.4 x 10^-2

(a)

128.

Convert this number into scientific notation:

950,000

a)

9.5 x 10⁵

b)

9.5 x 10^-9

c)

9.5 x 10²

d)

None of the above

129.

Which value is the greatest?

a)

5.0 x 10^-9

b)

5.0 x 10^-4

c)

5.0 x 10⁶

d)

5.0 x 10⁸

130.

Which number is the least in value?

a)

5.0 x 10^-9

b)

5.0 x 10^-4

c)

5.0 x 10⁶

d)

5.0 x 10⁸

131.

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

132.

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

Power rules and and Scientific Notation practice

Total questions: 132

Worksheet time: 4hrs 56mins

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