Free Printable Exponents, Roots, and Notations

1.

4²= ?

a)

16

b)

8

c)

42

d)

2

2.

$\left(\frac{4}{8}\right)^2$ = ?

a)

$\frac{8}{16}$

b)

$\frac{16}{8}$

c)

$\frac{16}{64}$

3.

^{Write in exponential form}8 · 8 · 8 · 8 · 8 · 8 · 8

a)

8⁸

b)

8⁷

c)

7⁸

d)

8⁹

4.

^{Write in expanded form:}
5⁴

a)

5 · 4

b)

5 · 5 · 5 · 5 ·

c)

4 · 4 · 4 · 4 · 4

d)

4 · 5 · 4 · 5

5.

^Compare6² ___ 2⁶

a)

>

b)

<

c)

=

6.

^Compare8²___ 2⁶

a)

>

b)

<

c)

=

7.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

8.

Which number is the EXPONENT?
4^{2 =}16

a)

4

b)

2

c)

16

9.

7 + (12-3)²

a)

256

b)

88

c)

10

d)

13

10.

(15 ÷ 3)² + 9 ÷ 3

a)

11.3

b)

28

c)

13

11.

2n⁴ * 5n⁴

a)

7n⁴

b)

10n¹⁶

c)

10n⁸

d)

none of the above

12.

(3c²)(10c⁷)

a)

13c⁹

b)

30c⁵

c)

30c⁹

d)

-30c⁹

13.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

14.

Simplify: 54y¹⁰÷ 6y⁵

a)

⁹y¹⁵

b)

y⁵⁰

c)

9y²

d)

9y⁵

15.

(-20x⁷y⁵) ÷ (-4x³y²)

a)

-5x⁴y³

b)

5x⁴y³

c)

5x¹⁰y⁷

d)

-5x¹⁰y⁷

16.

Simplify.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

17.

Simplify.

-4a^-2 ⋅ 2ab³

a)

b)

c)

d)

18.

Simplify.

a)

b)

c)

d)

19.

Simplify.

a)

10x¹¹y⁹

b)

c)

d)

20.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

21.

Any number written to the 0 power is always 1
Example: 8⁰=1

a)

True

b)

False

22.

How would you represent 8⁶ ?

a)

8 x 6

b)

8 x 8 x 6

c)

8 x 8 x 8 x 8 x 8 x 8

d)

6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

23.

m ⋅ m⁵⋅ m⁶

a)

m³⁰

b)

m¹²

c)

12m

d)

mm¹¹

24.

$x^{-5}$ =

a)

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

b)

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

c)

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

d)

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

25.

The product rule says that when you are multiplying two exponents with the same base, you keep the base and ________ the exponents

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

26.

$\frac{a^5b^{10}}{a^3b^6}=$

a)

$a^8b^{16}$

b)

$a^2b^4$

c)

$a^{15}b^{60}$

d)

$a^2b^{16}$

27.

$\frac{9x^2}{3x^{ }}=$

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

28.

$\frac{x^{17}}{x^8}$

a)

$x^9$

b)

$x^{25}$

c)

$x^{-9}$

d)

$x^{-25}$

29.

$\frac{x^9}{x^4}$ =

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^{-5}$

30.

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

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

a)

add

b)

subtract

c)

multiply

d)

divide

31.

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

a)

$x^{14}$

b)

$x^9$

c)

$x^5$

d)

$2x^7$

32.

$\left(a^3b^5\right)^7$ =

a)

$a^3b^{35}$

b)

$a^{10}b^{12}$

c)

$a^8b^8$

d)

$a^{21}b^{35}$

33.

$\left(ab^2\right)^8$ =

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

34.

When writing a number in scientific notation, the first number must be greater than 1, but less than 10.

a)

False

b)

True

35.

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

36.

How do you write
8.317 x 10⁶in standard form?

a)

8, 371, 000

b)

83, 170, 000

c)

837, 100

d)

8, 317, 000

37.

Write 0.000972 in scientific notation.

a)

9.72 x 10^-4

b)

9.72 x 10^-3

c)

972 x 10^-4

d)

9.72 x 10⁴

38.

Write 7.113 x 10⁷ in standard form.

a)

71,130,000

b)

7,113,000

c)

0.0000007113

d)

7,113

39.

Write 0.037 in scientific notation.

a)

3.7 x 10^-2

b)

3.7 x 10²

c)

37 x 10^-3

d)

37 x 10³

40.

How do you write
8.317 x 10⁶in standard form?

a)

8, 371, 000

b)

83, 170, 000

c)

837, 100

d)

8, 317, 000

41.

Write 0.00000707 in scientific notation.

a)

7.07 x 10^-6

b)

7.07 x 10⁶

c)

707 x 10⁸

d)

707 x 10^-8

42.

Which of the following is correct scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

43.

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

44.

Express the 0.000034 in Engineering notation

a)

3.4*10^-4

b)

3.4*10^-5

c)

34*10^-6

d)

340*10^-7

45.

Express 34000000 in Engineering notation

a)

3.4*10⁷

b)

3.4*10⁶

c)

34*10⁶

d)

340*10⁵

46.

Express 0.00021 in Engineering notation

a)

0.21*10^-3

b)

210*10^-6

c)

21*10^-5

d)

2.1*10^-4

47.

Express 4782000 in Engineering notation

a)

4.782*10⁶

b)

47.82*10⁵

c)

478.2*10⁴

d)

4782*10³

48.

Express number
100400 in engineering notation

a)

1.004*10⁵

b)

10.04*10⁴

c)

100.4*10³

d)

10004*10²

49.

10¹²

a)

tera

b)

pico

c)

giga

d)

nano

50.

10³

a)

micro

b)

mega

c)

kilo

d)

milli

51.

10⁶

a)

micro

b)

mega

c)

kilo

d)

milli

52.

10^-3

a)

micro

b)

mega

c)

kilo

d)

milli

53.

10^-6

a)

micro

b)

mega

c)

kilo

d)

milli

54.

10^-12

a)

tera

b)

pico

c)

giga

d)

nano

55.

10^-9

a)

tera

b)

pico

c)

giga

d)

nano

56.

Which of these items is ordered correctly, smallest to largest?

a)

giga, kilo, mega, tera

b)

kilo, giga, mega, tera

c)

kilo, mega, giga, tera

d)

tera, giga, kilo, mega

57.

Which prefix means 1 x 10^-3?

a)

Centi

b)

Milli

c)

Femto

d)

Micro

58.

Which prefix means 1 x 10⁹?

a)

Mega

b)

Tera

c)

Kilo

d)

Giga

59.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

60.

√64

a)

3

b)

8

c)

7

d)

6

61.

The square root of 256 is...

a)

15

b)

18

c)

13

d)

16

62.

True or false? 9² is 18

a)

True

b)

False

63.

Square root of 16 is....

a)

8

b)

4

c)

2

d)

3

64.

Which is equivalent to √121p⁵r⁷s⁴?

a)

11prs √pr

b)

11p^2.5r^3.5s²√pr

c)

11p²r³s²√pr

d)

11p²r³s²

65.

Simplfiy

a)

5√2

b)

0

c)

2√2

d)

-3√2

66.

Simplify

a)

√5

b)

-3√6

c)

√6

d)

6

67.

Simplify

a)

40

b)

√14

c)

-10√10

d)

2√10

68.

a)

A

b)

B

c)

C

d)

D

69.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

70.

a)

3√3x

b)

3√x

c)

2√3x

d)

2√x

71.

1)

a)

A

b)

B

c)

C

d)

D

72.

.

a)

A

b)

B

c)

C

d)

D

73.

Simplify:

a)

81√3

b)

9√3

c)

3√3

d)

√3

74.

√300 + √75

a)

15√3

b)

√375

c)

20√5

d)

16√5

75.

2√18a⁶b²

a)

3a³b√2

b)

6a³b²√2

c)

6a³b√2

d)

2a³b√2

76.

Simplify:

a)

A

b)

B

c)

C

d)

D

77.

Read the question carefully and choose the correct answer.

a)

A

b)

B

c)

C

d)

D

78.

Simplify completely.

a)

3v√2v

b)

3v√2v³

c)

v√18v

d)

9v√v

79.

Simplify the expression:

a)

25x²y³

b)

-5xy² ∛5x

c)

5ixy² ∛5x

d)

-125x³y⁶ ∛5x

80.

Simplify the expression:

a)

√2 - 3√3

b)

2√-59

c)

-2√2 - 3√3

d)

-3.782

81.

Simplify √40

a)

4√10

b)

10√4

c)

2√10

d)

10√2

82.

Simplify completely.

a)

8√3xy

b)

y√24xy

c)

8y√3xy

d)

8√24x

83.

Simplify.

a)

b)

c)

d)

84.

Simplify.

a)

b)

c)

d)

85.

Simplify $\sqrt{25n^2}$

a)

$5n\sqrt{n}$

b)

$n^2\sqrt{5}$

c)

$5n^2\sqrt{n}$

d)

$5n$

Exponents, Roots, and Notations

Total questions: 85

Worksheet time: 21hrs 15mins

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