Free Printable A1-CHAPTER 6 TEST

1.

Which of the following is in exponenetial form?

a)

5 x 5 x 5

b)

5³

c)

125

2.

Which of the following is in expanded form?

a)

5 x 5 x 5

b)

5³

c)

125

3.

Which of the following is in standard form?

a)

25

b)

5²

c)

5 X 5

4.

Write

7^5

in expanded form

a)

7 x 2

b)

526

c)

7x 7 x 7 x 7 x 7

d)

35

5.

$10^{2\ }$ Identify the base

a)

10

b)

2

6.

$10^2$ Identify the exponent

a)

10

b)

2

7.

$4^2$

How would you say this?

a)

"Four Squared"

b)

"Four Cubed"

8.

$5^3$ How would you say this?

a)

"Five cubed"

b)

"Five squared"

9.

5 x 5 x 5

What is this form called?

a)

Expanded Form

b)

Exponential Form

10.

7 x 7 x 7
How is this written in exponential form?

a)

$7^3$

b)

$3^7$

11.

$2^4$ How is this written in exponential form?

a)

2 x 2 x 2 x 2

b)

4 x 4

12.

$4^5$

What is this in expanded form?

a)

5 x 5 x 5 x 5

b)

4 x 4 x 4 x 4

c)

5 x 5 x 5 x 5 x 5

d)

4 x 4 x 4 x 4 x 4

13.

$2^4$ Is equivalent to?

a)

8

b)

20

c)

16

d)

12

14.

What is nine cubed in exponential form?

a)

9 x 9 x 9

b)

$9^3$

15.

$2^{5\ }$ is the same as 2 x 5.

a)

True

b)

False

16.

$8^6$

What number is the base on this:

a)

6

b)

68

c)

86

d)

8

17.

$4^3$ What is the BASE?

a)

4

b)

3

c)

$4^3$

d)

64

18.

$8^{0\ }=1$

Any number written to the 0 power is always 1

a)

True

b)

False

19.

$2^{7\ }$ or $7^2$

Which is GREATER?

a)

$2^7$

b)

$7^2$

c)

Neither, they are equal

20.

A scientist reports that a bacteria culture contains three to the forth power bacteria. How many bacteria is that?

a)

12

b)

81

c)

7

d)

95

21.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

22.

Which number is the EXPONENT?

4^{2 =}16

a)

4

b)

2

c)

16

23.

Identify the base:

$4^3$

(a)

24.

Identify the exponent: $5^2$

(a)

25.

How would you write in expanded form

8⁶ ?

a)

8 x 6

b)

8 x 8 x 6

c)

8 x 8 x 8 x 8 x 8 x 8

d)

6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

26.

Write $7^5$ in expanded form

a)

7 x 2

b)

7x 7 x 7 x 7 x 7

c)

526

d)

35

27.

$4^{3\ }$

Write in expanded form:

a)

4x4x4

b)

4+4+4

c)

3x3x3x3

d)

3+3+3+3

28.

$2^4$

Write in expanded form:

a)

4x4

b)

4+4

c)

2x2x2x2

d)

2+2+2+2

29.

Which equations with exponential expressions are true

a)

3²= 3 • 3

b)

4⁴ = 4 • 4

c)

5⁴ = 4 • 4 • 4 • 4 • 4

d)

7 • 7 • 7 • 7 • 7 • 7 = 7⁶

e)

9³= 9 • 9 • 9

30.

(¹/₂)²

a)

¹/₄

b)

1

c)

¹/₂

d)

¹/₈

31.

(¹/₅)²

a)

¹/₁₀

b)

²/₁₀

c)

²/₂₅

d)

¹/₂₅

32.

(¹/₃)³

a)

¹/₂₇

b)

¹/₉

c)

¹/₆

d)

¹/₃

33.

Challenge #2 (²/₃)²

a)

²/₆

b)

²/₉

c)

⁴/₆

d)

⁴/₉

34.

a)

6/8

b)

9/8

c)

6/16

d)

9/16

35.

a)

1/8

b)

1/6

c)

3/6

d)

3/8

36.

a)

8/18

b)

16/81

c)

16/18

d)

8/81

37.

a)

20/22

b)

100/22

c)

20/121

d)

100/121

38.

a)

1/6

b)

1/36

c)

2/12

d)

1/12

39.

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

a)

$\frac{3}{4}$

b)

$\frac{6}{8}$

c)

$\frac{9}{16}$

d)

$\frac{30}{40}$

40.

(0.2)²

a)

0.4

b)

0.2

c)

0.04

d)

0.02

41.

(0.3)²

a)

0.9

b)

0.06

c)

0.6

d)

0.09

42.

EVALUATE. WRITE YOUR ANSWER AS A DECIMAL OR WHOLE NUMBER.

$\left(0.03\right)^4$

(a)

43.

EVALUATE. WRITE YOUR ANSWER AS A DECIMAL OR WHOLE NUMBER.

$\left(0.1\right)^3$

(a)

44.

EVALUATE. WRITE YOUR ANSWER AS A DECIMAL OR WHOLE NUMBER.

$\left(0.03\right)^3$

(a)

45.

EVALUATE. WRITE YOUR ANSWER AS A DECIMAL OR WHOLE NUMBER.

$\left(0.63\right)^0$

(a)

46.

Rewrite using a positive exponent.
7^-10

a)

¹/_7¹⁰

b)

7¹⁰

c)

¹/_7^-10

d)

-70

47.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

48.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

¹/_w¹³

c)

¹/_w^-13

d)

w¹³

49.

Rewrite each expression with a negative exponent.
¹/_12⁴

a)

¹/_12^-4

b)

12⁴

c)

¹/_20,736

d)

12^-4

50.

Rewrite each expression with a negative exponent.
¹/₁₂₅

a)

¹/_5³

b)

5³

c)

5^-3

d)

¹/_5-3

51.

Write with positive exponents:

a)

a^-2

b)

a²

c)

1/a¹

52.

Rewrite so that there are no negative exponents in your final answer:

$6^{-4}$

a)

$-6^4$

b)

$\frac{1}{6^4}$

c)

$\frac{1}{4^6}$

d)

$-4^6$

53.

Rewrite so that there are no negative exponents in your final answer:

$\frac{1}{13^{-8}}$

a)

$\frac{1}{13^8}$

b)

$\frac{1}{-13^8}$

c)

$13^8$

d)

$-13^8$

54.

Write each expression

using a positive exponent.

2^{-3}

a)

$\frac{1}{-6}$

b)

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

c)

$-\frac{1}{8}$

d)

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

55.

Write the expression using a positive exponent.

m^{-4}

a)

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

b)

$-m^4$

c)

$\frac{1}{-m^4}$

d)

$\frac{1}{m^{-4}}$

56.

Simplify.
$y^{-2}$

a)

$\frac{4}{y^2}$

b)

$\frac{y}{2}$

c)

$\frac{2}{y}$

d)

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

57.

Simplify the expression so there are no negative exponents.
$9^{-2}$

a)

$-9^2$

b)

$9^2$

c)

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

d)

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

58.

Simplify the expression so there are no negative exponents.
$5^{-3}$

a)

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

b)

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

c)

$-5^3$

d)

$5^3$

59.

Write in simplified exponent form with no negative exponents.

$\frac{1}{8^{-4}}$

a)

$\frac{1}{8^4}$

b)

$-\frac{1}{8^4}$

c)

$8^4$

d)

$-8^4$

60.

Simplify:
b²⋅ b⁴

a)

b⁸

b)

b⁶

c)

b²

d)

2b⁶

61.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

62.

Multiply

a)

100

b)

10¹

c)

10^-2

d)

1/100

63.

Rewrite the expression as a power.
(2⁴)(2⁵)

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

64.

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

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

65.

r²⋅ r

a)

r³

b)

r²

c)

2r³

d)

11r²

66.

x^{20 .} x¹⁰

a)

x³⁰

b)

x²⁰⁰

c)

2x³⁰

d)

x¹⁰

67.

4 * 4²

a)

4²

b)

16²

c)

4³

d)

16³

68.

Simplify
m⁵⋅m²

a)

m⁷

b)

m³

c)

m¹⁰

d)

m²

69.

x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

70.

Simplify: $3^2\cdot3^4$

a)

$3^6$

b)

$3^8$

c)

$3^2$

d)

$3^{-2}$

71.

Simplify: $5\cdot5^3$

a)

$5^1$

b)

$5^2$

c)

$5^3$

d)

$5^4$

72.

Simplify: $7^9\cdot7^{-5}$

a)

$7^4$

b)

$7^{-45}$

c)

$\frac{1}{7^{45}}$

d)

$7^{14}$

73.

a)

y¹⁶

b)

y³

c)

16y

d)

y⁴⁸

74.

a)

5^-8

b)

5²

c)

25^-8

d)

25²

75.

a)

9^-4

b)

9^-45

c)

3^-4

d)

3^-45

76.

Solve using the product law of exponents.

(Espanol) Resolver utilizando la ley de productos de los exponentes.

(10¹²)(10⁴)

a)

10¹⁶

b)

10⁴⁸

c)

100¹⁶

d)

100⁴⁸

77.

Simplify.

Simplificar.

(x⁴) (x)

a)

2x⁴

b)

x

c)

x⁵

d)

x⁴

78.

Use the product law to solve.

Utilice la ley de productos para resolver.

(7^-17)(7^-24)

a)

7 ^-7

b)

49⁶⁹⁷

c)

7 ^-41

d)

49 ^-41

79.

Solve and leave answer as exponent.

Resolver y dejar la respuesta como exponente.

(8ⁿ)(8²)

a)

64²ⁿ

b)

8^{(2 + n)}

c)

8³

d)

8²ⁿ

80.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

81.

a)

x⁴

b)

x⁸

c)

x¹²

d)

x²⁰

82.

Simplify
x⁰

a)

x

b)

⁰

c)

1

d)

Undefined

83.

a)

1¹⁰

b)

1²⁶

c)

z¹⁰

d)

z²⁶

84.

a)

y¹⁴

b)

y¹⁰

c)

1¹⁴

d)

1¹⁰

85.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

86.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

87.

3⁴/ 3⁸

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

88.

a)

1¹⁶

b)

1⁶

c)

13¹⁶

d)

13⁶

89.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

90.

a)

b)

c)

d)

91.

a)

b)

c)

d)

92.

$\frac{y^{-7}}{y^{-13}}\ =\ ?$

a)

$y^{-6}$

b)

$y^6$

c)

$y^{-20}$

d)

$y^{20}$

93.

8¹⁶/8¹²

a)

8⁴

b)

8²⁸

c)

64⁴

d)

64²⁸

94.

6¹² ÷ 6⁶

a)

6⁶

b)

6¹⁸

c)

36⁶

d)

36¹⁸

95.

(5²)³

a)

5⁶

b)

5⁵

c)

5⁷

d)

5⁸

96.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

97.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

98.

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

99.

(ab)²

a)

ab²

b)

a²b²

c)

a²b

100.

Simplify

a)

\frac{x^{28}y^{12}}{x^2y}

b)

$\frac{x^{28}y^{12}}{x^8y^4}$

c)

$x^{20}y^8$

101.

(x⁵y⁴z³)²

a)

x¹⁰y⁸z⁶

b)

x⁷y⁶z⁵

c)

x¹⁰y⁶z⁵

d)

x²⁵y¹⁶z⁹

102.

Simplify: $\ \left(y^3\right)^{-2}$

a)

$y^1$

b)

$y^{-6}$

c)

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

d)

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

103.

Simplify: (y^-4)^-2

a)

y⁶

b)

y⁸

c)

y^-6

d)

y^-8

104.

(5²)³

a)

5⁶

b)

5⁵

c)

5⁷

d)

5⁸

105.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

106.

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

107.

Simplify:

$\left(7^3\right)^5$

a)

$7^8$

b)

$7^{15}$

c)

$7^2$

d)

$7^{35}$

108.

Simplify:

$\left(11^6\right)^3$

a)

$11^{63}$

b)

$11^3$

c)

$11^{18}$

d)

$11^9$

109.

Simplify:

$\left(z^5\right)^8$

a)

$z^{40}$

b)

$z^{13}$

c)

$z^{58}$

d)

$z^3$

110.

Find the missing exponent:

$10^{33}\ =\left(10^?\right)^3$

a)

11

b)

3

c)

30

d)

36

111.

$\left(2^4\right)^4$ Name the exponent you will see when you simplify using the power of a power rule.

(a)

112.

Exponent Rules: Zero Rule

x^{0\ }=_{ }

a)

0

b)

1

c)

x

d)

$0^x$

113.

Exponent Rules: Power of a Product

\left(ab\right)^x=

a)

$a^x+b^x$

b)

$a^{bx}$

c)

$a^xb^x$

114.

Exponent Rules: Negative Exponent

a^{-x}=

a)

$-a^{-x}$

b)

$-a^x$

c)

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

d)

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

115.

Simplify the following:
$\left(x^3y\right)^2$

a)

$x^5y^2$

b)

$x^6y^2$

c)

$x^1y^{-1}$

d)

$2x^3y$

116.

$\left(x^{\frac{1}{2}}y^{\frac{1}{4}}z^{\frac{1}{3}}\right)^{12}\ =$

Simplify the following:

a)

$x^{12.5}y^{12.25}z^{12.33}$

b)

$12\left(x^{\frac{1}{2}}y^{\frac{1}{4}}z^{\frac{1}{3}}\right)$

c)

$x^6y^3z^4$

117.

Simplify: $8^{\frac{2}{3}}$

a)

4

b)

2

c)

8

d)

$\frac{16}{3}$

118.

Biology: The approximate number of Calories C that an animal needs each day is given by $C=72m^{\frac{3}{4}}$

where m is the animal's mass in kilograms.

How many Calories does a 625 kg bear need to eat each day?

a)

900

b)

6000

c)

125

d)

9000

119.

$\left(8x^9\right)^{\frac{2}{3}}$

a)

$22x^{\frac{27}{2}}$

b)

$8x^6$

c)

$4x^6$

d)

$x^6$

120.

Simplify:

\left(8x^9\right)^{-\frac{2}{3}}

a)

$\frac{1}{4x^6}$

b)

$-4x^6$

c)

$4x^{-6}$

121.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

122.

Simplify:

a)

2

b)

8

c)

16

d)

32

123.

Simplify:

a)

2

b)

4

c)

8

d)

16

124.

(x^2/3)⁴

a)

x^8/3

b)

x^8/12

c)

x⁸

d)

x³

125.

a)

A

b)

B

c)

C

d)

D

126.

a)

A

b)

B

c)

C

d)

D

127.

a)

A

b)

B

c)

C

d)

D

128.

a)

A

b)

B

c)

C

d)

D

129.

a)

A

b)

B

c)

C

d)

D

130.

Simplify: $\left(x^{\frac{5}{3}}y^{-2}\right)^0$

a)

$1$

b)

$\frac{x^{\frac{5}{3}}}{y^2}$

c)

$x^{\frac{5}{3}}y^2$

d)

$\frac{y^2}{x^{\frac{5}{3}}}$

131.

$25^{-\frac{1}{2}}=?$

a)

$5$

b)

$-5$

c)

$-\frac{1}{5}$

d)

$\frac{1}{5}$

132.

Simplify the following: $\left(\frac{2x^3}{3x}\right)^{-2}$

a)

$\frac{9}{4x^4}$

b)

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

c)

$\frac{9x^3}{4}$

d)

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

133.

a)

1/4

b)

1/16

c)

-16

d)

-4

134.

Exponent Rules: Power of a Product

\left(ab\right)^x=

a)

$a^x+b^x$

b)

$a^{bx}$

c)

$a^xb^x$

135.

Simplify the following:
$\left(x^3y\right)^2$

a)

$x^5y^2$

b)

$x^6y^2$

c)

$x^1y^{-1}$

d)

$2x^3y$

136.

Biology: The approximate number of Calories C that an animal needs each day is given by $C=72m^{\frac{3}{4}}$

where m is the animal's mass in kilograms.

How many Calories does a 625 kg bear need to eat each day?

a)

900

b)

6000

c)

125

d)

9000

137.

$\left(8x^9\right)^{\frac{2}{3}}$

a)

$22x^{\frac{27}{2}}$

b)

$8x^6$

c)

$4x^6$

d)

$x^6$

138.

Simplify:

\left(8x^9\right)^{-\frac{2}{3}}

a)

$\frac{1}{4x^6}$

b)

$-4x^6$

c)

$4x^{-6}$

139.

(x^2/3)⁴

a)

x^8/3

b)

x^8/12

c)

x⁸

d)

x³

140.

a)

A

b)

B

c)

C

d)

D

141.

Simplify: $\left(x^{\frac{5}{3}}y^{-2}\right)^0$

a)

$1$

b)

$\frac{x^{\frac{5}{3}}}{y^2}$

c)

$x^{\frac{5}{3}}y^2$

d)

$\frac{y^2}{x^{\frac{5}{3}}}$

142.

Simplify the following: $\left(\frac{2x^3}{3x}\right)^{-2}$

a)

$\frac{9}{4x^4}$

b)

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

c)

$\frac{9x^3}{4}$

d)

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

143.

$\left(ab^2\right)^8$ =

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

A1-CHAPTER 6 TEST

Total questions: 143

Worksheet time: 5hrs 34mins

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