Free Printable Indices

1.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

2.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

3.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

4.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

5.

Simplify 4⁰

a)

1

b)

4

c)

0

6.

Simplify 4⁷ ÷ 4³

a)

4¹⁰

b)

4

c)

4²¹

d)

4⁴

7.

Write (4⁷ x 4³) ∕ 4⁴ as a single power

a)

4¹⁴

b)

4¹

c)

4⁸

d)

4⁶

8.

Evaluate 1² + 2² + 3²

a)

6

b)

12

c)

14

d)

11

9.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

10.

Simplify

a)

A

b)

B

c)

C

d)

D

11.

Simplify

a)

A

b)

B

c)

C

d)

D

12.

a×a×a

a)

3a

b)

3a³

c)

a³

d)

3a²

13.

a³×a⁴

a)

7a

b)

12a

c)

a¹²

d)

a⁷

14.

9a+a

a)

9a²

b)

9a

c)

10a

d)

11a

15.

a×a×a×a

a)

4a

b)

a⁴

c)

4a⁴

d)

2a²

16.

a²×a⁴

a)

6a

b)

6a²

c)

a⁶

d)

8a²

17.

5a×3a

a)

15a²

b)

30a

c)

15a

d)

a³⁰

18.

a×a⁸

a)

a⁸

b)

2a⁸

c)

a⁹

d)

2a⁹

19.

7a+3a

a)

21a²

b)

10a²

c)

21a

d)

10a

20.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

21.

Simplify

a)

10x³

b)

x⁴ / 2

c)

x³

d)

x³ / 2

22.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

23.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

24.

Simplify 4⁰

a)

1

b)

4

c)

0

25.

Write (4⁷ x 4³) ∕ 4⁴ as a single power

a)

4¹⁴

b)

4¹

c)

4⁸

d)

4⁶

26.

Calculate 3a⁸ x 4a²

a)

12a¹⁰

b)

12a¹⁶

c)

7a¹⁰

d)

7a¹⁶

27.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

28.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

29.

a)

z¹

b)

1

c)

0

d)

z^-1

30.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

31.

a)

x²

b)

x⁶

c)

x⁵

d)

x^-6

32.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

33.

a)

z¹

b)

1

c)

0

d)

z^-1

34.

a)

a⁷

b)

a¹

c)

1/a¹²

d)

a¹²

35.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

36.

a)

12

b)

8

c)

4

d)

2

37.

a)

x^-4

b)

1/x²

c)

x¹⁰

d)

x⁴

38.

a)

x⁴

b)

4x³

c)

3x³

d)

4x²

39.

a)

3a¹⁵

b)

9a¹⁵

c)

9a⁸

d)

27a¹⁵

40.

a)

3y⁶

b)

6y³

c)

4y⁶

d)

3y⁴

41.

a)

1/4

b)

2/3

c)

2

d)

0.5

42.

a)

1/7

b)

7

c)

24.5

d)

-7

43.

a)

3

b)

9

c)

12

d)

6

44.

a)

1/16

b)

1/9

c)

1/3

d)

1/27

45.

a)

1

b)

1/x

c)

x

d)

x^-11

46.

Simplify -9⁰

a)

1

b)

-1

c)

-9

d)

9

47.

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

a)

-8

b)

-6

c)

6

d)

8

48.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

49.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

50.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

51.

Simplify

a)

A

b)

B

c)

C

d)

D

52.

Simplify the following
3²x 2⁵x 3⁶x 2⁸

a)

3⁸x 2¹²

b)

3¹² x 2⁸

c)

3⁸x 2¹³

d)

2⁸x 3 ¹²

53.

2⁵÷ 2²

a)

1

b)

2³

c)

2⁷

d)

2¹²

54.

Simplify
3s⁴x 2t²x s³

a)

5st¹⁴

b)

5s⁷t²

c)

12 s⁷t ²

d)

6 s⁷t²

55.

a)

3a¹⁵

b)

9a¹⁵

c)

9a⁸

d)

27a¹⁵

56.

Simplify...

a)

a⁹

b)

a²⁰

c)

a¹

d)

a^-1

57.

Simplify...

a)

a¹⁵

b)

a⁴⁴

c)

a⁷

d)

a^-7

58.

Simplify...

a)

a¹²

b)

a²⁷

c)

a⁶

d)

a^-6

59.

Simplify...

a)

a¹⁰

b)

a²⁴

c)

a²

d)

a^-2

60.

Simplify...

a)

a¹⁷

b)

a⁷⁰

c)

a³

d)

a^-3

61.

Simplify...

a)

a^-2

b)

a²

c)

a^-8

d)

a⁸

62.

Simplify...

a)

a^-5

b)

a⁵

c)

a^-1

d)

a¹

63.

Simplify...

a)

a^-9

b)

a⁹

c)

a^-7

d)

a⁷

64.

Simplify...

a)

y²

b)

y¹²

c)

y^-2

d)

y³⁵

65.

Simplify...

a)

y¹²

b)

y⁷

c)

y^--12

d)

y¹⁶

66.

Simplify...

a)

y^-4

b)

y⁴

c)

y^-12

d)

y^0.5

67.

Simplify...

a)

y^-7

b)

y³

c)

y^-0.4

d)

y⁷

68.

Simplify...

a)

y^-5

b)

y^-11

c)

y⁵

d)

y²⁴

69.

Simplify...

a)

y^-13

b)

y^-3

c)

y³

d)

y^-1.6

70.

Simplify...

a)

m¹⁵

b)

m⁸

c)

m²

d)

m^-2

71.

Simplify...

a)

m²⁸

b)

m¹¹

c)

m^-3

d)

m²¹

72.

Simplify...

a)

m^-6

b)

m⁶

c)

m¹

d)

m^-1

73.

Simplify...

a)

m^-16

b)

m¹⁶

c)

m¹

d)

m⁰

74.

Simplify...

a)

m²⁰

b)

m^-20

c)

m^-9

d)

m¹

75.

Simplify...

a)

m¹⁶

b)

m^-16

c)

m^-10

d)

m^-6

76.

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

77.

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

78.

What is the correct law for powers of powers? (a^m)ⁿ =

a)

a^mxn

b)

a^m+n

c)

a^m x aⁿ

d)

a^men

79.

Simplify: 3⁵ x 3⁷

a)

3¹²

b)

9¹²

c)

3³⁵

d)

9³⁵

80.

Simplify: 2⁸ ÷ 2²

a)

2⁶

b)

2⁴

c)

2¹⁰

d)

1

81.

Simplify: f⁰

a)

1

b)

f

c)

f¹

d)

0

82.

Simplify: 3x³ × 6x⁸

a)

18x¹¹

b)

18x²⁴

c)

9x¹¹

d)

9x²⁴

83.

Simplify: 42m¹² ÷ 7m⁶

a)

6m⁶

b)

6m²

c)

35m⁶

d)

35m²

84.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

85.

Simplify: 64x¹⁶y¹² ÷ 4x⁸y³

a)

16x⁸y⁹

b)

16x²y⁴

c)

60x⁸y⁹

d)

60x²y⁴

86.

Simplify: (y⁷)²

a)

y¹⁴

b)

y⁴⁹

c)

y⁵

d)

y⁹

87.

Simplify: (3h²)³

a)

27h⁶

b)

27h⁵

c)

9h⁶

d)

9h⁵

88.

Simplify: (3a²b)² × (2ab)³

a)

72a⁷b⁵

b)

6a⁷b⁵

c)

36a⁵b⁴

d)

18a⁴b²

89.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

90.

Simplify: (3x)² × (2x³y)² ÷ 6y³

a)

6x⁸y^-1

b)

6x⁸y

c)

3x⁷y

d)

3x⁷y^-1

91.

Simplify

a)

10x³

b)

x⁴ / 2

c)

x³

d)

x³ / 2

92.

Simplify -9⁰

a)

1

b)

-1

c)

-9

d)

9

93.

Simplify -5p⁰t^-5/ 2^-1m²

a)

-5p/2t⁵m²

b)

10m²/t⁵

c)

(-5)(2)/t⁵m²

d)

-10/t⁵m²

94.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

95.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

96.

Calculate 11a⁵ x 8a⁷

a)

88a¹²

b)

88a³⁵

c)

19a¹²

d)

19a³⁵

97.

Find a^-80 ÷ a⁸

a)

a^-88

b)

a¹⁰

c)

a⁸⁸

d)

a^-72

98.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

99.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

100.

What is the missing index?(2⁶)^x = 2¹⁸

a)

12

b)

3

c)

10

d)

4

101.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

102.

a)

z¹

b)

1

c)

0

d)

z^-1

103.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

104.

Simplify,

(z³yx) × (x²yz)

a)

z⁴y²x³

b)

6 zyx

c)

3z 2y 3x

d)

z²÷ x

105.

Simplify:

25 x ⁶

5 x ³

a)

20x³

b)

5x⁹

c)

5x³

106.

$\left(6a^8b\right)\left(10a^3b^4\right)$

a)

$60a^5b^{-3}$

b)

$60a^{24}b^4$

c)

$16a^{11}b^5$

d)

$60a^{11}b^5$

107.

a)

$a^7$

b)

$a^1$

c)

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

d)

$a^{12}$

108.

Evaluate the expression using the quotient rule.

a)

$2^{14}z^{13}$

b)

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

c)

$\frac{2^{14}}{z^7}$

d)

$2^2z^7$

109.

Simplify (3a^-1c^-5)/ d⁰

a)

1

b)

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

c)

$\frac{3a}{c^5}$

d)

$\frac{1}{3a^1c^5d}$

110.

Simplify (34x⁵y⁶z^-7)⁰

a)

$\frac{34x^5y^6}{z^7}$

b)

$\frac{34x^5y^6}{x^{-7}}$

c)

0

d)

1

111.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

112.

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

113.

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

114.

What is the correct law for powers of powers? (a^m)ⁿ =

a)

a^mxn

b)

a^m+n

c)

a^m x aⁿ

d)

a^men

115.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

116.

Simplify 4⁰

a)

1

b)

4

c)

0

117.

2m⁵n³÷ 3m²n

a)

2/3 m⁵n²

b)

2/3 m³n²

c)

6 m³n²

d)

2/3 m²n3

118.

Simplify
3s⁴x 2t²x s³

a)

5st¹⁴

b)

5s⁷t²

c)

12 s⁷t ²

d)

6 s⁷t²

119.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

120.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

121.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

122.

a×a⁸

a)

a⁸

b)

2a⁸

c)

a⁹

d)

2a⁹

123.

Simplify: (3x)² × (2x³y)² ÷ 6y³

a)

6x⁸y^-1

b)

6x⁸y

c)

3x⁷y

d)

3x⁷y^-1

124.

a×a⁸

a)

a⁸

b)

2a⁸

c)

a⁹

d)

2a⁹

125.

What is the missing index?(2⁶)^x = 2¹⁸

a)

12

b)

3

c)

10

d)

4

126.

What is the Exponent form of $2\times\ 2\ \times\ 2\times2\times2$

a)

$2^5$

b)

$5^2$

c)

32

d)

16

127.

What is the value of $x^2\times\ x^{-3}\ \times\ x\ ^4$

a)

$x^9$

b)

$x^7$

c)

$x^6$

d)

$x^3$

128.

What is the value of $\left(5x\right)^0$

a)

$1x$

b)

$1$

c)

$0$

d)

undefined

129.

what is the value of $0^0$

a)

1

b)

0

c)

undefined

d)

none of above

130.

simplify $\frac{a^6\times a^7}{a^{13}}$

a)

$a^{26}$

b)

1

c)

0

d)

-1

131.

Evaluate $4x^3\ \times\ 2x^{-3}\$

a)

1

b)

0

c)

6

d)

8

132.

Find the value of $3^2\times10^2$

a)

900

b)

300

c)

600

d)

60

133.

Write $5x\times5x\times5x\times5x\$ in exponent form

a)

$5x^4$

b)

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

c)

$625x$

d)

$none$

134.

$Simplify:\ \ \ \ x^{m-n}\ \times\ x^{n-p\ }\times x^{p-n}$

a)

$x^{2m+2n+2p}$

b)

$1$

c)

0

d)

$x^m\ \times x^{n\ }\times x^p$

135.

$What\ is\ the\ value\ of\ \left(2^2\right)^3$

a)

64

b)

32

c)

8

d)

16

136.

$What\ is\ the\ value\ of\frac{1}{2^{-2}}\ ?$

a)

$\frac{1}{4}$

b)

$4$

c)

$\frac{1}{4}$

d)

0

137.

What is the Exponent form of $2\times\ 2\ \times\ 2\times2\times2$

a)

$2^5$

b)

$5^2$

c)

32

d)

16

138.

What is the value of $x^2\times\ x^{-3}\ \times\ x\ ^4$

a)

$x^9$

b)

$x^7$

c)

$x^6$

d)

$x^3$

139.

What is the value of $\left(5x\right)^0$

a)

$1x$

b)

$1$

c)

$0$

d)

undefined

140.

what is the value of $0^0$

a)

1

b)

0

c)

undefined

d)

none of above

141.

simplify $\frac{a^6\times a^7}{a^{13}}$

a)

$a^{26}$

b)

1

c)

0

d)

-1

142.

Evaluate $4x^3\ \times\ 2x^{-3}\$

a)

1

b)

0

c)

6

d)

8

143.

Find the value of $3^2\times10^2$

a)

900

b)

300

c)

600

d)

60

144.

Write $5x\times5x\times5x\times5x\$ in exponent form

a)

$5x^4$

b)

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

c)

$625x$

d)

$none$

145.

$Simplify:\ \ \ \ x^{m-n}\ \times\ x^{n-p\ }\times x^{p-n}$

a)

$x^{2m+2n+2p}$

b)

$1$

c)

0

d)

$x^m\ \times x^{n\ }\times x^p$

146.

$What\ is\ the\ value\ of\ \left(2^2\right)^3$

a)

64

b)

32

c)

8

d)

16

147.

$What\ is\ the\ value\ of\frac{1}{2^{-2}}\ ?$

a)

$\frac{1}{4}$

b)

$4$

c)

$\frac{1}{4}$

d)

0

148.

Simplify 10⁰

a)

10

b)

1

c)

0

d)

100

149.

Simplify 3^-3

a)

-27

b)

-9

c)

-1/9

d)

1/27

150.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

151.

Simplify 6⁵ x 6 x 6³

a)

6⁸

b)

216⁸

c)

6⁹

d)

216⁹

152.

Simplify 5³ x 5⁴

a)

5¹²

b)

5⁷

c)

25¹²

d)

25⁷

153.

Simplify 4⁷ ÷ 4³

a)

4¹⁰

b)

4

c)

4²¹

d)

4⁴

154.

Write 2 x 2 x 2 x 2 in index form

a)

4²

b)

2⁵

c)

16

d)

2⁴

155.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

d)

1²

156.

Simplify 5³ x 5⁴

a)

5⁷

b)

25⁷

c)

5¹²

d)

25¹²

157.

Simplify 6²⁰÷ 6⁵

a)

6¹⁵

b)

6²⁵

c)

15

d)

6⁴

158.

Simplify (4²)³

a)

64²

b)

4⁹

c)

4⁵

d)

4⁶

159.

Simplify (2³)⁵

a)

2¹⁵

b)

2⁸

c)

32¹⁵

d)

32⁵

160.

Simplify (-8)^-2

a)

1/(-8)²

b)

1/8^-2

c)

1/64

d)

-64

161.

Simplify 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

162.

Simplify (-4)⁰

a)

-4

b)

1/4

c)

-1

d)

1

163.

Simplify -9⁰

a)

1

b)

-1

c)

-9

d)

9

164.

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

a)

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

b)

$x^2$

c)

$x^{-2}$

d)

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

165.

64^⅓=

a)

4

b)

8

c)

6

d)

21.3

166.

Evaluate

a)

3

b)

18

c)

9

d)

6

167.

How else could you write $4^{-2}$ ?

a)

$16$

b)

$-16$

c)

$-\frac{1}{16}$

d)

$\frac{1}{16}$

168.

4^-½=

a)

2

b)

-2

c)

½

d)

-½

169.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

170.

Write the product using exponents:

(-2) ⋅ (-2) ⋅ (-2) ⋅ (-2) ⋅ (-2)

a)

-2⁵

b)

2^-5

c)

(-2)⁵

d)

(-2)^-5

171.

What comes next?
2^{2 =} 2x2
2³=2x2x2
2⁴=2x2x2x2

a)

2⁵=2x2x2x2

b)

2⁵=2x2x2x2x2

c)

2⁶=2x2x2x2x2x2

d)

2⁶⁼2x2x2x2x2

172.

What is 9^½

a)

3

b)

4.5

c)

81

d)

18

173.

8^⅓=

a)

2

b)

4

c)

6

d)

2.666

174.

What is 3^-1

a)

⅓

b)

½

c)

¼

d)

-3

175.

a)

3

b)

9

c)

12

d)

6

176.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

177.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

178.

Simplify 4⁰

a)

1

b)

4

c)

0

179.

Simplify 4⁷ ÷ 4³

a)

4¹⁰

b)

4

c)

4²¹

d)

4⁴

180.

Evaluate 1² + 2² + 3²

a)

6

b)

12

c)

14

d)

11

181.

a³×a⁴

a)

7a

b)

12a

c)

a¹²

d)

a⁷

182.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

183.

3²x 3⁵

a)

3⁶

b)

3⁷

c)

3⁸

d)

3¹⁰

184.

q⁶ x q ^-6

a)

q¹

b)

q²

c)

q¹²

d)

1

185.

a)

3a¹⁵

b)

9a¹⁵

c)

9a⁸

d)

27a¹⁵

186.

Write 6 x 6 x 6 in index notation.

a)

$6^3$

b)

$6^6$

c)

$6^{18}$

d)

$6^2$

187.

Write 15 x 15 x 15 x 15 x 15 x 15 x 15 in index notation.

a)

$15^{15}$

b)

$15^7$

c)

$15^5$

d)

$7^{15}$

188.

Write s x s x s x s in index notation.

a)

$s^1$

b)

$s^2$

c)

$s^3$

d)

$s^4$

189.

Write j x j x j x j x j x j x j x j x j x j in index notation.

a)

$j^9$

b)

$j^j$

c)

$j^{10}$

d)

$j^8$

190.

Write $3^5$ as a product of prime factors.

a)

3 x 5 x 3 x 5

b)

5 x 5 x 5

c)

3 x 3 x 3 x 3

d)

3 x 3 x 3 x 3 x 3

191.

Write $b^7$ as a product of prime factors.

a)

b x b x b x b x b x b x b

b)

b x 7 x b x 7 x b x 7 x b

c)

7 x 7 x 7 x 7 x 7 x 7 x 7

d)

7b x 7b x 7b x 7b x 7b x 7b x 7b

192.

Write 8 x 8 in index form using 2 as the base.

a)

$2^2\ \ \times\ \ 4^2$

b)

2 x 4 x 2 x 4

c)

$2^6$

d)

2 x 2 x 2 x 2 x 2 x 2

193.

Write 9 x 9 in index form using 3 as the base.

a)

3 x 3 x 3 x 3

b)

$3^4$

c)

$9^2$

d)

3 x 9 x 3 x 9

194.

Challenging Question

Write 625 in index form using 5 as the base.

a)

25 x 25

b)

$5^4$

c)

5 x 5 x 5 x 5

d)

$25^2$

195.

Express $w^{-5}$ as a positive index.

a)

5w x 5w x 5w x 5w x 5w

b)

w x w x w x w x w

c)

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

d)

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

196.

Express $4\ a^{-6}$ as a positive index.

a)

4a x 4a x 4a x 4a x 4a x 4a

b)

$\frac{4}{a^{-6}}$

c)

$\frac{4}{a^6}$

d)

4 x a x a x a x a x a x a

197.

Express $9^{-2}\ \ h^{-7}$ as a positive index.

a)

$\frac{1}{9^2\ h^7}$

b)

$\frac{1}{9^{-2}\ \ h^{-7}}$

c)

$\frac{9^2}{h^7}$

d)

$\frac{h^7}{9^2}$

198.

Simplify $3^2\ \ \times\ \ 3^{-7}$ as positive index.

a)

$3^5$

b)

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

c)

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

d)

$3^{-5}$

199.

Simplify $f^{-4}\ \times\ \ f^5$ as positive index.

a)

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

b)

$\frac{f^{-4}}{f^5}$

c)

$f^{-1}$

d)

$f$

200.

Simplify and express $6^{3\ }\div\ 6^5$ in positive index form.

a)

$6^2$

b)

$\frac{6\ \ \times\ \ 6\ \ \times\ \ 6}{6\ \ \times\ \ 6\ \ \times\ \ 6\ \ \times\ \ 6\ \ \times\ \ 6}$

c)

$6^{-2}$

d)

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

201.

Simplify and express $y^8\ \ \div\ \ y^2$ in positive index form.

a)

$y^6$

b)

$y^{-6}$

c)

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

d)

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

202.

Simplify and express $\left(10^2\right)^{-1}$ as a positive index.

a)

$10^{-2}$

b)

$10^2$

c)

$\frac{1}{10^2}$

d)

$\frac{1}{10^{-2}}$

203.

Simplify and express $\left(x^{-2}\right)^5$ as positive index.

a)

$x^{10}$

b)

$x^{-10}$

c)

$\frac{1}{x^{10}}$

d)

$\frac{1}{x^{-10}}$

204.

Simplify and express $5\ \left(n^2\right)^{-3}$ as positive index.

a)

$\frac{5}{n^6}$

b)

$5\ \ \times\ \ n^6$

c)

$5\ \ \times\ \ n^{-6}$

d)

$\frac{n^6}{5}$

205.

Simplify and express $10\ \left(q^{-5}\right)^3$ as a positive index.

a)

$10\ \times\ q^{-15}$

b)

$10\ \ \times\ \ q^{15}$

c)

$\frac{10}{q^{15}}$

d)

$\frac{10}{q^{-15}}$

206.

3²x 3⁵

a)

3⁶

b)

3⁷

c)

3⁸

d)

3¹⁰

207.

2b⁶ x 2b¹³

a)

2b¹⁹

b)

2b⁹

c)

4b¹⁹

d)

4b¹²

208.

Simplify the following
3²x 2⁵x 3⁶x 2⁸

a)

3⁸x 2¹²

b)

3¹² x 2⁸

c)

3⁸x 2¹³

d)

2⁸x 3 ¹²

209.

Find the value
3x 4²x 3²

a)

3³x 4²

b)

4³x 3²

c)

434

d)

432

210.

2⁵÷ 2²

a)

1

b)

2³

c)

2⁷

d)

2¹²

211.

a⁵÷ a⁵

a)

a¹

b)

a⁵

c)

1

d)

a

212.

6a⁵÷ 2a²

a)

3a³

b)

12a³

c)

4a¹⁰

d)

2a⁷

213.

2m⁵n³÷ 3m²n

a)

2/3 m⁵n²

b)

2/3 m³n²

c)

6 m³n²

d)

2/3 m²n3

214.

36a⁸b⁷÷ 30ab³

a)

5/6 a⁸b⁴

b)

6/5 a⁷b³

c)

6/5 a³b⁷

d)

5/6 a⁷b³

215.

Simplify
3s⁴x 2t²x s³

a)

5st¹⁴

b)

5s⁷t²

c)

12 s⁷t ²

d)

6 s⁷t²

216.

Simplify: χ³ ÷ χ²

a)

χ

b)

χ⁵

c)

χ⁶

d)

χ^-1

e)

1/χ

217.

Evaluate 6⁴

a)

216

b)

24

c)

1296

d)

6 x 6 x 6 x 6

218.

Evaluate 2³+ 3²

a)

72

b)

36

c)

12

d)

17

219.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

220.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

221.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

222.

Simplify 4⁰

a)

1

b)

4

c)

0

223.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

224.

Find a^-80 ÷ a⁸

a)

a^-88

b)

a¹⁰

c)

a⁸⁸

d)

a^-72

225.

Find the value
3x 4²x 3²

a)

3³x 4²

b)

4³x 3²

c)

434

d)

432

226.

6a⁵÷ 2a²

a)

3a³

b)

12a³

c)

4a¹⁰

d)

2a⁷

227.

36a⁸b⁷÷ 30ab³

a)

5/6 a⁸b⁴

b)

6/5 a⁷b³

c)

6/5 a³b⁷

d)

5/6 a⁷b³

228.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

229.

a)

x²

b)

x⁶

c)

x⁵

d)

x^-6

230.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

231.

$\left(6a^8b\right)\left(10a^3b^4\right)$

a)

$60a^5b^{-3}$

b)

$60a^{24}b^4$

c)

$16a^{11}b^5$

d)

$60a^{11}b^5$

232.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

233.

What is the area of a rectangle with dimensions listed below:

length = 10x⁷

width = 7x⁵

a)

70x¹²

b)

70x³⁵

c)

17x¹²

d)

17x³⁵

234.

State the term for number 6.

a)

Base

b)

Index

c)

Power

d)

Multiple

235.

State the term for number 3.

a)

Index

b)

Base

c)

Integer

d)

Multiple

236.

Repeated multiplication is

a)

multiply the same number for certain times

b)

multiply number for three times

c)

repeat the multiplication non-stop

237.

5 X 5 X 5 X 5 X 5 X 5 in index form is

a)

5⁵

b)

5⁶

c)

6⁵

d)

6⁶

238.

m x m x m x m x m x m x m = m⁷

a)

True

b)

False

239.

Which of the following are number in index form?

a)

64

b)

(3/4)⁵

c)

(0.2)³

d)

3 : 5

240.

Convert (-5)³ into repeated multiplication.

a)

(-5) x (-5) x (-5)

b)

- (5 x 5 x 5)

c)

(-5) x 3

d)

- (5 x 3)

241.

How to convert a number into number in index form

a)

Repeated division method

b)

Repeated multiplication method

c)

Repeated addition method

d)

Repeated subtraction method

242.

Convert 512 to an index number with base 8

a)

8³

b)

64

c)

8⁴

d)

8 x 8 x 8

243.

Which of the following have the same value with 4096 ?

a)

8⁴

b)

4⁶

c)

16³

d)

32²

244.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

245.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

246.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

247.

a)

z¹

b)

1

c)

0

d)

z^-1

248.

a)

a⁷

b)

a¹

c)

1/a¹²

d)

a¹²

249.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

250.

a)

3a¹⁵

b)

9a¹⁵

c)

9a⁸

d)

27a¹⁵

251.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

252.

Choose the correct rules of indices

a)

$a^m\times a^n=a^{m+n}$

b)

$a^m+a^n=a^{mn}$

c)

$\left(a^m\right)^n=a^{mn}$

d)

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

e)

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

253.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

Indices

Total questions: 253

Worksheet time: 6hrs 1mins

Similar Resources on Wayground