Free Printable Laws of Indices

1.

What is the correct law for multiplication? a^m x aⁿ=

a)

a^m+n

b)

a^m + aⁿ

c)

a^mxn

d)

a^mⁿ

2.

What is the correct law for division? a^m ÷ aⁿ =

a)

a^m-n

b)

a^m - aⁿ

c)

a^m÷n

d)

a^m/n

3.

Simplify: 3⁵ x 3⁷

a)

3¹²

b)

9¹²

c)

3³⁵

d)

9³⁵

4.

Simplify: 2⁸ ÷ 2²

a)

2⁶

b)

2⁴

c)

2¹⁰

d)

1

5.

Simplify: f⁰

a)

1

b)

f

c)

f¹

d)

0

6.

Simplify: (3x²y³)⁰

a)

1

b)

0

c)

3x²y³

d)

3

7.

Simplify: 3x³ × 6x⁸

a)

18x¹¹

b)

18x²⁴

c)

9x¹¹

d)

9x²⁴

8.

Simplify: 42m¹² ÷ 7m⁶

a)

6m⁶

b)

6m²

c)

35m⁶

d)

35m²

9.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

10.

Simplify: 64x¹⁶y¹² ÷ 4x⁸y³

a)

16x⁸y⁹

b)

16x²y⁴

c)

60x⁸y⁹

d)

60x²y⁴

11.

Simplify: (3h²)³

a)

27h⁶

b)

27h⁵

c)

9h⁶

d)

9h⁵

12.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

13.

Simplify: (2x²y)² × (3xy³)⁰

a)

4x⁴y²

b)

12x⁴y²

c)

4x⁵y⁵

d)

12x⁵y⁵

14.

Simplify: (3x)² × (2x³y)² ÷ 6y³

a)

6x⁸y^-1

b)

6x⁸y

c)

3x⁷y

d)

3x⁷y^-1

15.

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

a)

$\left(x\div1\right)^4$

b)

$x^{\left(4\div1\right)}$

c)

$x^{\left(4-0\right)}$

d)

$x^{\left(4-1\right)}$

16.

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

a)

$\left(\frac{x}{y}\right)^4$

b)

$\left(x-y\right)^4$

c)

$\left(\frac{x}{y}\right)^{\left(4-4\right)}$

d)

$x^4-y^4$

17.

$4x^3\ \times3y^2\ =$

a)

$12x^5$

b)

$12y^5$

c)

$12xy^5$

d)

$12x^3y^2$

18.

What is $a^{\frac{1}{3}}$ ?

a)

$^3\sqrt{a}$

b)

$\sqrt{a}$

c)

$a\times\frac{1}{3}$

d)

$a\div\frac{1}{3}$

19.

Evaluate: $81^{\frac{3}{4}}$

(a)

20.

$^4\sqrt{3^5}$ is equal to

a)

$3^{\frac{4}{5}}$

b)

$3^{\frac{5}{4}}$

c)

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

d)

$3^{\frac{1}{4}}$

21.

Evaluate: $9^{-2}$

a)

$\frac{1}{81}$

b)

$-\frac{2}{9}$

c)

$-\frac{1}{81}$

d)

$\frac{2}{9}$

e)

$-81$

22.

64^⅓=

a)

4

b)

8

c)

6

d)

21.3

23.

What is 9^½

a)

3

b)

4.5

c)

81

d)

18

24.

Evaluate: $2^{-5}$

a)

$\frac{1}{32}$

b)

$-\frac{5}{2}$

c)

$-\frac{1}{32}$

d)

$-\frac{2}{5}$

e)

$-16$

25.

Write the product using exponents:

(-2) ⋅ (-2) ⋅ (-2) ⋅ (-2) ⋅ (-2)

a)

-2⁵

b)

2^-5

c)

(-2)⁵

d)

(-2)^-5

26.

How else can you write $\sqrt{x}$ ?

a)

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

b)

$x^2$

c)

$x^{-2}$

d)

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

27.

What is 3^-1

a)

⅓

b)

½

c)

¼

d)

-3

28.

Evaluate

a)

3

b)

18

c)

9

d)

6

29.

Evaluate the following...

(fully simplify your answer)

a)

⁴⁹/₈₁

b)

⁹/₇

c)

⁸¹/₄₉

d)

(⁹/₇)²

30.

$-9^2$ = _____

a)

81

b)

$-81$

c)

$\frac{1}{81}$

d)

$-\frac{1}{81}$

e)

$-18$

31.

What is 9^½

a)

3

b)

4.5

c)

81

d)

18

32.

Evaluate: $100^{\frac{5}{2}}$

(a)

33.

What is $8^{\frac{1}{3}}$ ?

a)

$\frac{8}{3}$

b)

24

c)

2

d)

$\frac{23}{3}$

34.

$^n\sqrt{a^m}$ or $\left(^n\sqrt{a}\right)^m$ is equal to ...

a)

$a^{\frac{m}{n}}$

b)

$a^{\frac{n}{m}}$

c)

$\frac{a^m}{a^n}$

d)

$\frac{a^n}{a^m}$

35.

$-9^{-2}$ = ___

a)

$81$

b)

$-81$

c)

$\frac{1}{81}$

d)

$-\frac{1}{81}$

e)

$-18$

36.

4^-½=

a)

2

b)

-2

c)

½

d)

-½

37.

Evaluate: $16^{\frac{3}{2}}$

(a)

38.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

39.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

40.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

41.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

42.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

43.

a)

1

b)

1/x

c)

x

d)

x^-11

44.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

45.

a)

b)

c)

d)

46.

a)

b)

c)

d)

47.

Write with positive exponents:

1/a^-2

a)

a^-2

b)

a²

c)

1/a¹

48.

xy⁰

a)

xy

b)

x

c)

1

d)

0

49.

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

a)

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

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

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

50.

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)

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

51.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

52.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

53.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

54.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

55.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

56.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

57.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

58.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

59.

When solving exponential equations, you must first get like _______?

a)

exponents

b)

bases

60.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

61.

Solve

a)

2

b)

-2

c)

3

d)

-3

62.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

63.

Solve

a)

-2

b)

6

c)

9

d)

3

64.

Solve

a)

-4

b)

5

c)

-3

d)

-5

65.

What is the base in the expressions.

a)

1

b)

2

c)

8

d)

1/8

66.

What is the exponent in the expressions?

a)

1

b)

2

c)

8

d)

1/8

67.

What is the base in the expressions.

a)

3

b)

7

c)

-3

d)

-7

68.

What is the graph of the equation

a)

b)

c)

d)

69.

What is the graph of the equation?

a)

b)

c)

d)

70.

Simplify

a)

b)

c)

d)

71.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

72.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

73.

Solve for x:
5^2x = 5^-x

a)

0

b)

-6

c)

8

d)

1

74.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

75.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

76.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

77.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

78.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

79.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

80.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

Laws of Indices

Total questions: 80

Worksheet time: 3hrs 5mins

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