Free Printable 8th Grade Properties of exponents

1.

a)

$\frac{1}{w^3}$

b)

w³

c)

w²

d)

$\frac{1}{w^{13}}$

2.

a)

x⁴y⁴

b)

x⁸y⁴

c)

$\frac{y^{12}}{x^4}$

d)

x⁸y¹²

3.

a)

0

b)

x

c)

1

d)

x¹²

4.

a)

$25x^{22}$

b)

$10x^{22}$

c)

$25x^{13}$

d)

$-25x^{22}$

5.

(x⁸)(x⁻⁵)

a)

$\frac{1}{x^{40}}$

b)

$\frac{1}{x^{13}}$

c)

x¹³

d)

x³

6.

a)

k⁷

b)

k³

c)

1/k¹⁰

d)

k¹⁰

7.

a)

b⁶

b)

b⁷

c)

b¹

d)

$\frac{1}{b^6}$

8.

a)

d²

b)

d⁸⁰

c)

d⁸¹⁰

d)

d¹⁸

9.

Simplify:

(2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

10.

Simplify the expression.

(xy)⁷

a)

x⁷y⁷

b)

xy⁷

c)

xy¹⁴

d)

$\frac{x^{7^{ }}}{y^7}$

11.

Simplify
(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

12.

(x⁶)³

a)

x⁹

b)

x²

c)

x⁶

d)

x¹⁸

13.

(4x³)²

a)

8x⁵

b)

8x⁶

c)

16x⁵

d)

16x⁶

14.

(3x⁴)(4x²)

a)

7x⁶

b)

12x⁶

c)

7x⁸

d)

12x⁸

15.

(-2x³)(-5x⁷)

a)

-10x²¹

b)

-10x¹⁰

c)

10x²¹

d)

10x¹⁰

16.

a)

$\frac{1}{16}$

b)

$\frac{1}{8}$

c)

-16

d)

-8

17.

a)

$\frac{1}{27}$

b)

$\frac{1}{-9}$

c)

27

d)

9

18.

a)

x⁷

b)

x¹¹

c)

$\frac{1}{x^{11}}$

d)

$\frac{1}{x^9}$

19.

a)

$\frac{1}{y^6}\$

b)

$\frac{1}{y^9}\$

c)

1

d)

0

20.

a)

$\frac{1}{z}\$

b)

$\frac{1}{z^{11}}\$

c)

z

d)

z¹¹

21.

(a⁴)⁶

a)

a⁴⁶

b)

a²⁴

c)

a¹⁰

22.

a⁶⋅ a⁴

a)

a⁶⁴

b)

a²⁴

c)

a¹⁰

23.

a²(a³)(a⁶)

a)

a¹¹

b)

a³⁶

c)

a20

d)

3a¹²

24.

(q²)(2q⁴)

a)

2q⁸

b)

2q⁶

c)

16q⁶

d)

16q⁸

25.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

26.

(-3y)³

a)

9y³

b)

-27y³

c)

-9y³

d)

-3y³

27.

(-2u²)(6u⁶)

a)

-12u⁸

b)

-12u¹²

c)

4u⁸

d)

4u¹²

28.

Simplify the expression.
x³x⁶

a)

x⁹

b)

x³

c)

x¹⁸

d)

x³⁶

29.

Make this negative exponent positive.

9^-3

a)

9³

b)

$\frac{1}{729}\$

c)

$\frac{1}{93}$

d)

729

30.

$\frac{x^8}{x^2}$

a)

x⁴

b)

x¹⁶

c)

$\frac{1}{x^6}$

d)

x⁶

31.

7⁰

a)

$\frac{1}{7}$

b)

0

c)

1

d)

7

32.

(3x)⁰

a)

(3x)¹

b)

0¹

c)

1

d)

3x

33.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

34.

a)

4a⁶

b)

4a⁵

c)

-4a⁶

d)

-4a⁵

35.

a)

$\frac{k^{12}}{9}$

b)

9k²

c)

$\frac{1}{9k^2}$

d)

$\frac{9}{k^2}$

36.

Simplify $\frac{4^6}{4^{-2}}$

a)

$\frac{1}{64}$

b)

$\frac{1}{256}$

c)

256

d)

65536

37.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

38.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

39.

Simplify the expression.
(3c)⁴

a)

81c⁴

b)

3⁴c⁴

c)

81c

d)

12c⁴

40.

(ab⁸c)(a^-17c¹⁰)

a)

a¹⁷b⁸c¹¹

b)

a¹⁶b⁸c¹¹

c)

$\frac{b^8c^{11}}{a^{16}}\ \ \$

d)

$\frac{b^8c^{10}}{a^{17}}\ \$

41.

a)

$\frac{1}{w^3}$

b)

w³

c)

w²

d)

$\frac{1}{w^{13}}$

42.

a)

x¹¹

b)

x¹⁸

c)

$\frac{1}{x^7}$

d)

x⁷

43.

a)

x⁴y⁴

b)

x⁸y⁴

c)

$\frac{y^{12}}{x^4}$

d)

x⁸y¹²

44.

Simplify: $\frac{x^{-9}}{x^{-3}}$

a)

x¹²

b)

x⁶

c)

$\frac{1}{x^6}$

d)

$\frac{1}{x^{12}}$

45.

a)

0

b)

x

c)

1

d)

x¹²

46.

Evaluate the expression using the quotient of powers rule.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

a⁸b⁷

47.

Simplify: $\frac{x^2}{x^{-5}}$

a)

x³

b)

$\frac{1}{x^3}$

c)

x⁷

d)

x¹⁰

48.

a)

$\frac{1}{r^4}$

b)

r⁴

c)

r²

d)

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

49.

(3⁴)(3^-7)

a)

81

b)

27

c)

$\frac{1}{81}$

d)

$\frac{1}{27}$

50.

Simplify.

5⁰

a)

5

b)

1

c)

0

d)

$\frac{1}{5}$

51.

a)

b⁶

b)

b⁷

c)

b¹

d)

b^-6

52.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

53.

(5x²)⁰(9x)²

a)

45x⁴

b)

81x

c)

81x²

d)

0

54.

Evaluate $11^{-2}$

a)

$\frac{1}{22}$

b)

-121

c)

$\frac{1}{121}$

d)

-22

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.

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

61.

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

62.

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

63.

Write 6,700 in scientific notation.

a)

6.7 x 10³

b)

6.7 x10^-3

c)

67 x 10²

d)

67 x 10^-2

64.

Write 7.113 x 10⁷ in standard form.

a)

71,130,000

b)

7,113,000

c)

0.0000007113

d)

7,113

65.

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

66.

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

67.

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

68.

Write the answer in scientific notation.

4.1 x 10⁶ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁶

c)

9.6 x 10¹²

d)

4.65 x 10⁵

69.

(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

70.

(7.7 x 10²) + (4.1 x 10²)=

a)

11.8 x 10¹

b)

1.18 x 10³

c)

11.8 x 10³

d)

1.18 x 10²

71.

(2 x 10^-5)+ (7 x 10^-5)

a)

9 x 10^-10

b)

14 x 10^-5

c)

9 x 10^-5

d)

1.4 x 10^-4

72.

(8 x 10⁴) + (4 x 10⁴)

a)

12 x 10⁴

b)

1.2 x 10⁵

c)

1.2 x 10⁹

d)

1.2 x 10⁸

73.

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)

1.1 x 10¹¹

d)

1.1 x 10 ⁶

74.

Solve:
(6.0 x 10⁴) + (3.0 x 10⁴)

a)

9.0 x 10⁴

b)

3.0 x 10⁴

c)

9.0 x 10⁸

d)

3.0 x 10⁰

75.

(8 x 10^-3)+ (7 x 10^-3)

a)

1.5 x 10^-3

b)

1.5 x 10^-4

c)

1.5 x 10^-2

d)

1.5 x 10^-6

8th Grade Properties of exponents

Total questions: 75

Worksheet time: 4hrs 40mins

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