Free Printable Exponent Rules, Rational Exponents, and Simplifying Radicals

1.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

2.

Simplify: $3n^5\cdot5n^{10}$

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

3.

$3^7\cdot3^7$

a)

$9^{49}$

b)

$3^{14}$

c)

$3^{49}$

d)

$9^{14}$

4.

Simplify: $10x^8\cdot9x$

a)

$90x^8$

b)

$19x^9$

c)

$90x^9$

d)

$19x^9$

5.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

6.

Simplify: $\frac{2^9}{2^6}$

a)

$1^3$

b)

$0^3$

c)

$2^3$

d)

$2^{15}$

7.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

8.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

9.

Simplify: $\left(4y\right)^{-3}$

a)

$\frac{1}{64y^3}$

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

$\frac{64}{y^3}$

10.

Simplify: $\left(2m\right)^5$

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

$\frac{1}{2m^5}$

11.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

12.

Simplify: $\left(-x^3\right)\left(-5x\right)$

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

13.

Simplify: $\frac{k^3}{5k}$

a)

$5k^2$

b)

$\frac{5}{k^2}$

c)

$\frac{k^2}{5}$

d)

$\frac{k^4}{5}$

14.

Simplify: $\left(3k^5\right)\left(-2k^3\right)$

a)

$6k^8$

b)

$-6k^{15}$

c)

$6k^{15}$

d)

$-6k^8$

15.

Simplify: $\left(\frac{4}{2d^2}\right)^3$

a)

$\frac{2}{d^2}$

b)

$\frac{8}{d^6}$

c)

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

d)

$\frac{64}{2d^2}$

16.

Simplify: $\frac{-15x^9}{10x^{17}}$

a)

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

b)

$\frac{-3x^8}{2}$

c)

$\frac{-3x^{-8}}{2}$

d)

$\frac{-3}{2x^8}$

17.

Simplify: $\frac{\left(4x^2y^3\right)^0}{8x^3}$

a)

$\frac{1}{8x^3}$

b)

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

c)

$\frac{4y^3}{8x}$

d)

$1$

18.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

19.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

20.

Simplify: $3n^5\cdot5n^{10}$

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

21.

$3^7\cdot3^7$

a)

$9^{49}$

b)

$3^{14}$

c)

$3^{49}$

d)

$9^{14}$

22.

Simplify: $10x^8\cdot9x$

a)

$90x^8$

b)

$19x^9$

c)

$90x^9$

d)

$19x^9$

23.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

24.

Simplify: $\frac{2^9}{2^6}$

a)

$1^3$

b)

$0^3$

c)

$2^3$

d)

$2^{15}$

25.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

26.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

27.

Simplify: $\left(4y\right)^{-3}$

a)

$\frac{1}{64y^3}$

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

$\frac{64}{y^3}$

28.

Simplify: $\left(2m\right)^5$

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

$\frac{1}{2m^5}$

29.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

30.

Simplify: $\left(-x^3\right)\left(-5x\right)$

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

31.

Simplify: $\frac{k^3}{5k}$

a)

$5k^2$

b)

$\frac{5}{k^2}$

c)

$\frac{k^2}{5}$

d)

$\frac{k^4}{5}$

32.

Simplify: $\left(3k^5\right)\left(-2k^3\right)$

a)

$6k^8$

b)

$-6k^{15}$

c)

$6k^{15}$

d)

$-6k^8$

33.

Simplify: $\left(\frac{4}{2d^2}\right)^3$

a)

$\frac{2}{d^2}$

b)

$\frac{8}{d^6}$

c)

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

d)

$\frac{64}{2d^2}$

34.

Simplify: $\frac{-15x^9}{10x^{17}}$

a)

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

b)

$\frac{-3x^8}{2}$

c)

$\frac{-3x^{-8}}{2}$

d)

$\frac{-3}{2x^8}$

35.

Simplify: $\frac{\left(4x^2y^3\right)^0}{8x^3}$

a)

$\frac{1}{8x^3}$

b)

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

c)

$\frac{4y^3}{8x}$

d)

$1$

36.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

37.

$3^{-3}$

a)

$27$

b)

$-27$

c)

$\frac{1}{-27}$

d)

$\frac{1}{27}$

38.

$2^{-5}$

a)

$-32$

b)

$32$

c)

$\frac{1}{32}$

d)

$\frac{1}{-32}$

39.

$4^3$

a)

$\frac{1}{64}$

b)

$-64$

c)

$64$

d)

$\frac{1}{-64}$

40.

a)

2^1/6

b)

64

c)

6^1/2

d)

2⁶

41.

Write the expression in exponential form:
√23

a)

23^1/2

b)

23^-1/2

c)

23²

d)

23^-2

42.

Write the expression in radical form.

y^1/2

a)

√y

b)

∛y

c)

√y²

d)

∛y²

43.

Check all that is true

Simplify the expression:

36^1/2

a)

6

b)

$\sqrt{36}$

c)

-6

d)

1296

44.

Check all that is true

Simplify the expression:

27^1/3

a)

3

b)

9

c)

∛27

d)

3³

45.

Write as a radical expression
y¹⁄ ³

a)

∛y

b)

y³

c)

√y

d)

1∕ 3y

46.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

47.

$8^{\frac{1}{3}}$ check at that applies

a)

24

b)

2

c)

cubed root of 8

d)

512

48.

Check all that applies

a)

8

b)

4

c)

1024

d)

256^1/4

49.

$5^{\frac{1}{2}}$

a)

$\sqrt{5}$

b)

10

c)

25

d)

$\sqrt{25}$

50.

$2^{\frac{1}{3}}$

a)

2

b)

cubed root of 3

c)

6

d)

cubed root of 2

51.

an exponent 1/2 means

a)

square root

b)

cube root

c)

fourth root

d)

fifth root

52.

Your exponents denominator is the (a) ?

53.

In the following, what is my base $\left(-2\right)^{\frac{1}{3}}$

a)

-2

b)

2

54.

$-2^{\frac{1}{6}}$

What is my base

a)

-2

b)

2

55.

$\sqrt{13}$

a)

$6$

b)

$13$

c)

$13^{\frac{1}{2}}$

d)

$13^2$

56.

What is the 5th root of 1024?

a)

5120

b)

4

c)

160

d)

32

57.

$512^{\frac{1}{3}}$

a)

8

b)

22

c)

1539

d)

171

58.

Bonus:

21z^{\frac{1}{2}}

a)

$21^2$ $z^2$

b)

21 $z^2$

c)

$\sqrt{21z}$

d)

21 $\sqrt{z}$

59.

Write using a rational exponent: $\sqrt[5]{x^3}$

a)

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

b)

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

c)

$x^2$

d)

$x^8$

60.

Write using a rational exponent: $\sqrt[3]{x^7}$

a)

$x^{\frac{7}{3}}$

b)

$x^{\frac{3}{7}}$

c)

$x^4$

d)

$x^{11}$

61.

Write using a rational exponent: $\sqrt[3]{x^6}$

a)

$x^2$

b)

$x^3$

c)

$x^9$

d)

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

62.

Write using a rational exponent: $\sqrt[5]{x^2}$

a)

$x^{\frac{2}{5}}$

b)

$x^{\frac{5}{2}}$

c)

$x^3$

d)

$x^7$

63.

Write using a rational exponent: $\sqrt[3]{x^8}$

a)

$x^{\frac{8}{3}}$

b)

$x^{\frac{3}{8}}$

c)

$x^5$

d)

$x^{11}$

64.

Write using a rational exponent: $\sqrt[]{x^{11}}$

a)

$x^{\frac{11}{2}}$

b)

$x^{11}$

c)

$x^9$

d)

$x^{10}$

65.

Write using a rational exponent: $\sqrt[]{x^5}$

a)

$x^{\frac{5}{2}}$

b)

$x^5$

c)

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

d)

$x^4$

66.

Write using a rational exponent: $\sqrt[]{x^{12}}$

a)

$x^6$

b)

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

c)

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

d)

$x^{12}$

67.

Write using a rational exponent: $\sqrt[]{x^8}$

a)

$x^8$

b)

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

c)

$x^4$

d)

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

68.

Write using a radical: $x^{\frac{3}{7}}$

a)

$\sqrt[7]{x^3}$

b)

$\sqrt[3]{x^7}$

c)

$\sqrt[]{x^{\frac{7}{3}}}$

d)

$x^4$

69.

Write using a radical: $x^{\frac{8}{5}}$

a)

$\sqrt[5]{x^8}$

b)

$\sqrt[8]{x^5}$

c)

$\sqrt[]{x^{\frac{5}{8}}}$

d)

$x^{-3}$

70.

Write using a radical: $x^{\frac{13}{7}}$

a)

$\sqrt[7]{x^{13}}$

b)

$\sqrt[13]{x^7}$

c)

$\sqrt[]{x^{\frac{7}{13}}}$

d)

$x^6$

71.

Write using a radical: $x^{\frac{1}{5}}$

a)

$\sqrt[5]{x^{ }}$

b)

$\sqrt[]{x^5}$

c)

$\sqrt[]{x^{\frac{1}{5}}}$

d)

$x^5$

72.

Write using a radical: $x^{\frac{1}{8}}$

a)

$\sqrt[8]{x^{ }}$

b)

$\sqrt[]{x^8}$

c)

$\sqrt[]{x^{\frac{1}{8}}}$

d)

$x^8$

73.

$x^0$

a)

$1$

b)

$0$

c)

$x$

d)

$\sqrt[]{x}$

74.

Write using a radical: $x^{\frac{1}{10}}$

a)

$\sqrt[10]{x^{ }}$

b)

$\sqrt[]{x^{10}}$

c)

$\sqrt[]{x^{\frac{1}{10}}}$

d)

$x^{10}$

75.

$\sqrt[3]{x^{15}}$

a)

$x^5$

b)

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

c)

$x^{12}$

d)

$x^{18}$

76.

$\sqrt[4]{x^{28}}$

a)

$x^7$

b)

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

c)

$x^{24}$

d)

$x^{-24}$

77.

Write using a radical: $x^{\frac{7}{2}}$

a)

$\sqrt[]{x^7}$

b)

$\sqrt[7]{x^2}$

c)

$\sqrt[]{x^{\frac{2}{7}}}$

d)

$x^5$

78.

Write using a radical: $x^{\frac{11}{2}}$

a)

$\sqrt[]{x^{11}}$

b)

$\sqrt[11]{x^2}$

c)

$\sqrt[]{x^{\frac{2}{11}}}$

d)

$x^9$

79.

√24 =

a)

4√6

b)

2√6

c)

6√2

d)

2√12

80.

√28 =

a)

7√2

b)

7√4

c)

4√7

d)

2√7

81.

√45 =

a)

3√5

b)

5√3

c)

9√5

d)

5√9

82.

√96 =

a)

16√6

b)

2√6

c)

4√6

d)

√2

83.

√125 =

a)

5√5

b)

25√5

c)

5√25

d)

5√2

84.

√216 =

a)

6√4

b)

4√6

c)

36√6

d)

6√6

85.

√169 =

a)

3√7

b)

13

c)

7√3

d)

7√7

86.

√243 =

a)

3√3

b)

9√3

c)

81√3

d)

3√81

87.

√80 =

a)

16√5

b)

2√20

c)

4√5

d)

8√5

88.

√75 =

a)

25√3

b)

25√3

c)

5√3

d)

3√5

89.

√18 =

a)

3√2

b)

9√2

c)

3√9

d)

2√3

90.

√1 =

a)

1

b)

2

c)

0

d)

1/2

91.

√16 =

a)

4

b)

8

c)

16

d)

64

92.

√300 =

a)

3√10

b)

2√150

c)

100√3

d)

10√3

93.

√32 =

a)

3√2

b)

4√8

c)

16√2

d)

4√2

94.

√ 49 =

a)

6

b)

7

c)

8

d)

9

95.

√40 =

a)

4√10

b)

10√4

c)

2√10

d)

10√2

96.

√256 =

a)

12√2

b)

9√14

c)

16

d)

18√6

97.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

98.

√36x³y⁴

a)

6y²x√x

b)

3y²√2x

c)

3y√x

d)

6x√3y

99.

-3√20x⁴y²

a)

-6x²y√5

b)

6xy√5

c)

-3xy√2

d)

3x²y√5

100.

$\sqrt{192k^7q^8}$

a)

$8q^4\sqrt{3k^7}$

b)

$8k^3q^4\sqrt{3}$

c)

$8k^3q^4\sqrt{3k}$

d)

$8k^7q^8\sqrt{3k}$

101.

Simplify $\sqrt{108}$

a)

$8\sqrt{2}$

b)

$6\sqrt{3}$

c)

$10\sqrt{8}$

d)

$2\sqrt{27}$

102.

√96p⁹

a)

4p³

b)

4p⁴√p

c)

4p⁴√6p

d)

4p⁴√2p

103.

In simplest radical form,
√80 is equivalent to

a)

16√5

b)

2√20

c)

4√5

d)

8√5

104.

Simplify 4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

105.

$\sqrt{4x^7y^5z^9}$ Simplify

a)

$2x^3y^2z^3\sqrt{xy}$

b)

$2z^3\sqrt{x^7y^5}$

c)

$2xyz\sqrt{x^6y^5z^8}$

d)

$2x^3y^2z^4\sqrt{xyz}$

106.

$\sqrt{216}$

a)

$6\sqrt{4}$

b)

$4\sqrt{6}$

c)

$36\sqrt{6}$

d)

$6\sqrt{6}$

Exponent Rules, Rational Exponents, and Simplifying Radicals

Total questions: 106

Worksheet time: 4hrs 32mins

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