Free Printable rational exp and laws

1.

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

a)

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

b)

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

c)

$x^2$

d)

$x^8$

2.

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

a)

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

b)

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

c)

$x^4$

d)

$x^{11}$

3.

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

a)

$x^2$

b)

$x^3$

c)

$x^9$

d)

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

4.

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

a)

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

b)

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

c)

$x^3$

d)

$x^7$

5.

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

a)

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

b)

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

c)

$x^5$

d)

$x^{11}$

6.

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

a)

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

b)

$x^{11}$

c)

$x^9$

d)

$x^{10}$

7.

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

a)

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

b)

$x^5$

c)

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

d)

$x^4$

8.

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

a)

$x^6$

b)

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

c)

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

d)

$x^{12}$

9.

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

a)

$x^8$

b)

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

c)

$x^4$

d)

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

10.

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)

$x^4$

11.

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)

$x^{-3}$

12.

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)

$x^6$

13.

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

a)

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

b)

$\sqrt[]{x^5}$

c)

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

d)

$x^5$

14.

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

a)

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

b)

$\sqrt[]{x^8}$

c)

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

d)

$x^8$

15.

$x^0$

a)

$1$

b)

$0$

c)

$x$

d)

$\sqrt[]{x}$

16.

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

a)

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

b)

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

c)

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

d)

$x^{10}$

17.

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

a)

$x^5$

b)

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

c)

$x^{12}$

d)

$x^{18}$

18.

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

a)

$x^7$

b)

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

c)

$x^{24}$

d)

$x^{-24}$

19.

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

a)

$\sqrt[]{x^7}$

b)

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

c)

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

d)

$x^5$

20.

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

a)

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

b)

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

c)

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

d)

$x^9$

21.

Re-write $\left(5xy\right)^{-\frac{1}{3}}$ in radical form.

a)

$\ ^3\sqrt{5xy}$

b)

$\frac{1}{\ ^3\sqrt{5xy}}$

c)

$\frac{1}{\left(5xy\right)^3}$

d)

$\frac{5}{\ ^3\sqrt{xy}}$

22.

Simplify
(6^3/4)^1/3

a)

6^1/4

b)

6^3/12

c)

6^4/7

d)

6^9/12

23.

$\sqrt{7}$ Which of the following is equivalent to the expression

a)

$\frac{1}{7^2}$

b)

$7^{\frac{1}{2}}$

c)

$7^{\frac{2}{1}}$

d)

$2^{\frac{1}{7}}$

e)

not given

24.

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

(a)

25.

$125^{\frac{1}{3}}$ Evaluate

a)

41.5

b)

$\frac{1}{125^3}$

c)

-5

d)

5

26.

$8^{\frac{2}{3}}$ Evaluate

a)

$\frac{16}{3}$

b)

$\frac{64}{3}$

c)

4

d)

$8\sqrt{3}$

27.

$27^{\frac{2}{3}}$ Evaluate

(a)

28.

Simplify:

a)

2

b)

4

c)

16

d)

64

29.

8^5/3

a)

64

b)

32

c)

16

d)

24

30.

a)

2^1/6

b)

64

c)

6^1/2

d)

2⁶

31.

Simplify the cube root.

$\sqrt[3]{40}$

a)

$2\sqrt[3]{5}$

b)

$5\sqrt[3]{8}$

c)

$2$

d)

$8\sqrt[3]{2}$

32.

Simplify the cube root.

$\sqrt[3]{40}$

a)

$2\sqrt[3]{5}$

b)

$5\sqrt[3]{8}$

c)

$2$

d)

$8\sqrt[3]{2}$

33.

According to exponent rules, when we multiply terms with the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

34.

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

a)

add

b)

subtract

c)

multiply

d)

divide

35.

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

a)

add

b)

subtract

c)

multiply

d)

divide

36.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

37.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

38.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

39.

Evaluate the expression using the quotient rule.

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

40.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

41.

Which expression is equivalent to the given?

a)

b)

c)

d)

42.

Which expression is equivalent to the given?

a)

b)

c)

d)

43.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

44.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

45.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

46.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

47.

Simplify with no negative exponents:
x^-3

a)

-3x

b)

x³

c)

1/ x^-3

d)

1/ x³

48.

Which expression is equivalent to the given?

a)

b)

c)

d)

49.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

50.

a)

a⁷

b)

a¹⁰

c)

a³

d)

a^-3

51.

Rewrite each expression with a negative exponent.
¹/_12⁴

a)

¹/_12^-4

b)

12⁴

c)

¹/_20,736

d)

12^-4

52.

Expand x⁵

a)

x⋅x⋅x⋅x⋅x

b)

1/x⋅x⋅x⋅x⋅x

c)

x⁵

d)

5

53.

Which of the following shows the PRODUCT rule of Exponents?

a)

$x^0=1$

b)

$\frac{x^a}{x^b}=x^{a-b}$

c)

$\left(x^a\right)^b=x^{a\cdot b}$

d)

$x^a\cdot x^b=x^{a+b}$

e)

$x^{-a}=\frac{1}{x^a}$

54.

Which of the following shows the POWER rule of Exponents?

a)

$x^0=1$

b)

$\frac{x^a}{x^b}=x^{a-b}$

c)

$\left(x^a\right)^b=x^{a\cdot b}$

d)

$x^a\cdot x^b=x^{a+b}$

e)

$x^{-a}=\frac{1}{x^a}$

55.

Which of the following shows the QUOTIENT rule of Exponents?

a)

$x^0=1$

b)

$\frac{x^a}{x^b}=x^{a-b}$

c)

$\left(x^a\right)^b=x^{a\cdot b}$

d)

$x^a\cdot x^b=x^{a+b}$

e)

$x^{-a}=\frac{1}{x^a}$

56.

Which of the following shows the ZERO EXPONENT rule of Exponents?

a)

$x^0=1$

b)

$\frac{x^a}{x^b}=x^{a-b}$

c)

$\left(x^a\right)^b=x^{a\cdot b}$

d)

$x^a\cdot x^b=x^{a+b}$

e)

$x^{-a}=\frac{1}{x^a}$

57.

Which of the following shows the NEGATIVE EXPONENT rule of Exponents?

a)

$x^0=1$

b)

$\frac{x^a}{x^b}=x^{a-b}$

c)

$\left(x^a\right)^b=x^{a\cdot b}$

d)

$x^a\cdot x^b=x^{a+b}$

e)

$x^{-a}=\frac{1}{x^a}$

58.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

59.

Simplify: (6m⁷)/(4m³)²

a)

(6m)/16

b)

(3/8)m

c)

3/(8m)

d)

(3m)/4

60.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

61.

5⁶written in standard form is

a)

6 x 6 x 6 x 6 x 6

b)

5 x 6

c)

5 x 5 x 5 x 5 x 5 x 5

d)

5 x 5

62.

Simplify:

12² x 2³ x 12⁵ x 2²

a)

12⁷ x 2⁵

b)

12¹⁰x 2⁶

c)

12⁵x 2¹⁰

d)

567⁶⁰

63.

Simplify: $\frac{n^{10}}{n^4\times n^6}$

a)

$n^{10}$

b)

$\frac{n^{10}}{n^{10}}$

c)

1

d)

0

64.

a)

m⁴

b)

m⁶

c)

m¹⁰

d)

1/m⁶

65.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

66.

a)

True

b)

False

67.

a)

b)

c)

d)

rational exp and laws

Total questions: 67

Worksheet time: 1hrs 19mins

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