Free Printable Chapter 7 Review

1.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

2.

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

a)

add

b)

subtract

c)

multiply

d)

divide

3.

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

a)

add

b)

subtract

c)

multiply

d)

divide

4.

How do you solve:
(2x⁵)(6x⁴)

a)

MULTIPLY coefficients
MULTIPLY exponents

b)

DIVIDE coefficients
SUBTRACT exponents

c)

Combine like terms

d)

MULTIPLY coefficients
ADD exponents

5.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

6.

x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

7.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

8.

3⁻⁴

a)

1 ⁄ 3⁴

b)

-3⁴

c)

3⁴

d)

1 ⁄ 12

9.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

10.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

11.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

12.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

13.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

14.

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

a)

add

b)

subtract

c)

multiply

d)

divide

15.

Write $7^5$ as repeated multiplication

a)

7 x 2

b)

7x 7 x 7 x 7 x 7

c)

526

d)

35

16.

$10^2$ Identify the base

a)

10

b)

2

17.

$10^2$ Identify the exponent

a)

10

b)

2

18.

Write the equation using exponents

3 X 3 X 3

a)

3¹

b)

3³

c)

3²

19.

Simplify the following:
(x³)⁶

a)

x⁹

b)

x¹⁸

c)

x⁶

d)

x³

20.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

21.

[ (12x³y⁵z⁷)/ (144x^-4 y⁷z^-3)]⁰

a)

12(x⁷z¹⁰)

b)

1

c)

(x⁷z¹⁰)/12y²

d)

(x⁷y^-2z¹⁰)/12

22.

a)

2x/y⁹

b)

3y²³/4

c)

3y²³/4x

d)

3x²³/y⁴

23.

a)

x^-7

b)

x⁷

c)

1/x⁷

d)

x^-9

24.

Which two exponent rules do you need to use to simplify this expression?

a)

Product Rule and Quotient Rule

b)

Power Rule and Product Rule

c)

Power Rule and Negative Exponent Rule

d)

Zero Rule and Power Rule

25.

(7pq)⁶

a)

$7^6\cdot\ p^6\ \cdot q^6$

b)

$7pq^6$

c)

42pq

26.

$\frac{8^5}{8^2}$

a)

$8^3$

b)

$8^7$

c)

$8^{10}$

27.

a)

y¹⁵

b)

y⁵⁰

c)

y²

d)

y⁵

28.

Simplify the exponential expression.

a)

8x⁴

b)

15x²

c)

15x⁴

d)

225x⁴

29.

Simplify the exponential expression.

a)

28x³

b)

28x¹¹

c)

11x¹¹

d)

11x³

30.

Simplify the exponential expression.

a)

m⁶⁵

b)

m¹¹

c)

m³⁰

d)

m⁷⁷⁷⁶

31.

Simplify the exponential expression.

a)

x⁹

b)

x⁴⁹

c)

x²

d)

x¹⁴

32.

Simplify the exponential expression.

a)

a⁶b¹⁵

b)

a¹⁸b

c)

a¹⁸b⁸

d)

a⁶b³

33.

Solve (hint: there's more than 1 law you must obey)

a)

x²⁸y¹² / x²y

b)

x²⁸y¹² / x⁸y⁴

c)

x²⁰y⁸

34.

Solve (hint: there's more than 1 law you must obey)

a)

4k⁴

b)

4k^-8

c)

4 / k⁸

35.

a)

2x/y⁹

b)

3y²³/4

c)

3y²³/4x

d)

3x²³/y⁴

36.

Simplify $\frac{5x^3}{2x^{-6}}$

a)

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

b)

$x^9$

c)

$\frac{5x^9}{2}$

d)

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

37.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

38.

Evaluate $5n^{-4}\cdot2n^6$

a)

$\frac{18}{n}$

b)

$\frac{12}{n^9}$

c)

$18n^7$

d)

$10n^2$

39.

Evaluate $x^3\cdot2x^{-6}$

a)

$24x^3$

b)

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

c)

$\frac{15}{x^3}$

d)

$6x^3$

40.

Simplify $\frac{5r^6}{4r^3}$

a)

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

b)

$\frac{3r}{2}$

c)

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

d)

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

41.

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

a)

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

b)

$x^{11}$

c)

$x^9$

d)

$x^{10}$

42.

Evaluate without a calculator.

a)

A

b)

B

c)

C

d)

D

43.

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

a)

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

b)

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

c)

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

d)

$x^{10}$

44.

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)

$x^6$

45.

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

a)

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

b)

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

c)

$x^5$

d)

$x^{11}$

46.

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

a)

$x^2$

b)

$x^3$

c)

$x^9$

d)

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

47.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

48.

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

a)

$x^5$

b)

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

c)

$x^{12}$

d)

$x^{18}$

49.

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

a)

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

b)

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

c)

$x^4$

d)

$x^{11}$

50.

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)

$x^{-3}$

51.

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

a)

$x^7$

b)

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

c)

$x^{24}$

d)

$x^{-24}$

52.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

53.

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

a)

$x^8$

b)

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

c)

$x^4$

d)

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

54.

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

a)

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

b)

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

c)

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

d)

$x^9$

55.

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

a)

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

b)

$\sqrt[]{x^8}$

c)

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

d)

$x^8$

56.

Solve the following using your laws of exponents.

3^{2x-1}=27

a)

Not here

b)

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

c)

$x=1$

d)

$x=2$

57.

Solve the following now!

\left(\frac{1}{4}\right)^{x-2}=64

a)

$x=6$

b)

$x=5$

c)

$x=-2$

d)

$x=-1$

58.

How would you write 4.3756 x 10⁴in standard form?

a)

437,560,000

b)

0.00043756

c)

43,756

d)

4,3756

59.

How would you write 0.0005 in scientific notation?

a)

50 x 10⁵

b)

5 x 10⁴

c)

5 x 10³

d)

.5 x 10³

60.

How would you write -5.6 x 10^-3 in standard form?

a)

0.0056

b)

-5,600

c)

0.00056

d)

-0.0056

61.

Scientific Notation is made up of two number parts. The first part should be a number between 1 and 100.

a)

True

b)

False

62.

Scientific Notation is made up of two number parts. The second part is a power of base 10.

a)

True

b)

False

63.

When writing a number in scientific notation, the first number must be greater than 1, but less than 10.

a)

False

b)

True

64.

The rule of scientific notation is to write all exponents with a base of ____.

a)

50

b)

5

c)

100

d)

10

65.

How do you write
1001
in scientific notation?

a)

1.0001 x 10⁴

b)

1.01 x 10⁵

c)

1.001 x 10³

d)

10.1 x 10³

66.

How do you write
8.317 x 10⁶in standard form?

a)

8, 371, 000

b)

83, 170, 000

c)

837, 100

d)

8, 317, 000

67.

Which of the following is correct scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

68.

Express the following in scientific notation:
.000457

a)

457 x 10⁶

b)

457 x 10^-6

c)

4.57 x10⁴

d)

4.57 x 10^-4

69.

Express the following in standard notation:
8.025 x 10^-⁸

a)

.00000008025

b)

.000000008025

c)

802,500,000,000

d)

80,250,000,000

70.

Express the following in scientific notation:
10,030,400,000

a)

1.00304 x 10⁹

b)

1.00304 x 10¹⁰

c)

1.00403 x 10¹⁰

d)

1.00304 x10^-10

71.

Express the following in scientific notation:
0.0000002203

a)

.02203 x 10⁷

b)

22.03 x 10^-6

c)

2.203 x 10^-7

d)

22.03 x 106

72.

Convert to scientific notation:
520,000,000

a)

52 x 10⁷

b)

5.2 x 10⁷

c)

5.2 x 10⁸

d)

0.52 x 10⁹

73.

Convert to standard notation:
2.4 x 10^-3

a)

2400

b)

0.24

c)

0.024

d)

0.0024

74.

Convert to standard notation:
3.05 x 10⁵

a)

305,000

b)

305

c)

3,050,000

d)

30,500

75.

What is scientific notation?

a)

A long way to write really short numbers

b)

A short way to write really long numbers

c)

I don't know...

d)

None of the above

76.

UNDERSTANDING
If the exponent is a positive number...

a)

you will get a large number

b)

you will get a smaller number

77.

UNDERSTANDING
If the exponent is a negative number...

a)

you will get a large number

b)

you will get a small number

78.

What is the simplified version of

a)

3.9 x 10⁶

b)

4 x 10²⁰

c)

4 x 10⁶

d)

3.9 x 10²⁰

79.

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

a)

30.08 x 10¹¹

b)

3.8 x 10¹

c)

3.008 x 10¹²

d)

2.9375 x 10¹

80.

(9.6×10³) × (6.7×10²)

a)

64.32×10⁵

b)

6.432×10⁶

c)

64.32×10⁶

d)

64.32×10⁵

81.

(2.5 x 10⁴) (4 x 10³)

a)

1.0 x 10⁷

b)

1.0 x 10⁸

c)

10 x 10⁷

d)

1.0 x 10⁶

82.

What is it called when you go from this form to this next form?
0.0088 to 8.8 x 10³

a)

Standard form to scientific notation

b)

Scientific notation to regular form

c)

Scientific notation to standard form

d)

Standard form to regular form

83.

5 x 10¹²
------------
2 x 10⁶

a)

2.5 x 10²

b)

2.5 x 10⁶

c)

3 x 10²

d)

2.5 x 10¹⁸

84.

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

a)

3 x 10¹⁰

b)

3 x 10⁴

c)

3 x 10^-4

d)

3 x 10^-11

85.

On the graph y = 4^x + 2.

What is the domain?

a)

x > 0

b)

x > 2

c)

x > 4

d)

All real numbers

86.

On the graph y = 3^x + 4 shown , what is the y=intercept?

a)

(0,1)

b)

(0,4)

c)

(0,5)

d)

There is no y-intercept

87.

Determine the horizontal asymptote for the function

f(x) = 3(2)^x-4+ 5

a)

x=4

b)

y=4

c)

x=5

d)

y=5

88.

Write the equation of the graph.

a)

f(x) = 5^x+ 2

b)

f(x) = 3^x - 2

c)

f(x) = 3^x + 2

d)

f(x) = -3^x +2

89.

Determine the range for the function.
$f\left(x\right)=2^{x-4}+5$

a)

y > 4

b)

y > 2

c)

y > 3

d)

y > 5

90.

The graph shows the number of game consoles sold in millions since 2009.

Based on this information, which function best models the number of game consoles sold in millions x years since 2009?

a)

$g\left(x\right)=0.6\left(25.5\right)^x$

b)

$g\left(x\right)=25.5\left(0.6\right)^x$

c)

$g\left(x\right)=6.12\left(25.5\right)^x$

d)

$g\left(x\right)=25.5\left(6.12\right)^x$

91.

An exponential function is graphed on the grid.

Which function is best represented by the graph?

a)

$p\left(x\right)=\left(0.25\right)^x$

b)

$p\left(x\right)=2\left(0.5\right)^x$

c)

$p\left(x\right)=\left(1.25\right)^x$

d)

$p\left(x\right)=\left(25\right)^x$

92.

Determine the y-intercept and asymptote for the following exponential function.

Hint: for the asymptote , just click which dot it would be, BE CAREFUL on this one!

A

B

C

D

E

93.

Graph the following function:

Hint: Don't forget to move the asymptote line!

$g\left(x\right)=4\left(\frac{1}{4}\right)^x-7$

94.

Graph the following function:

Hint: Don't forget to move the asymptote line!

$f\left(x\right)=5\left(\frac{1}{2}\right)^x$

95.

Graph the following function:

Hint: Don't forget to move the asymptote line!

$y=2^x$

96.

y= 3(2)^x

97.

Which are exponential functions? Select all that apply.

a)

b)

c)

d)

e)

98.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

c)

No Y-intercept

d)

y=1

99.

What is the equation that best represents the graph?

a)

y=2^y

b)

y=2^x

c)

y=2^-x

d)

y=x²

100.

Classify:

$f\left(x\right)=\frac{5}{4}\left(0.8\right)^x-9$

a)

Exponential Growth

b)

Exponential Decay

101.

y= 16 ( $\frac{1}{4}$ )^x

102.

In March, 2020, before the Covid-19 lockdown, 1,200,000 Texans had applied for unemployment. During the COVID-19 lockdown, the number of people applying for unemployment increased by 4% each month. What exponential function can be used to find the number of people applying for unemployment after x months of COVID-19 lockdown? (a)

Choose from the below words

$y=1,200,000\left(1.04\right)^x$

$y=\ 1,200,000\left(0.04\right)^x$

$y=1,200,000\left(1.4\right)^x$

$y=1,200,000\left(0.06\right)^x$

103.

Which of the following exponential functions represents an initial value of 1780 and a growth of 18% for x years?

(a)

Choose from the below words

$y=1780\left(1.18\right)^x$

$y=1780\left(0.18\right)^x$

$y=\ 1780\ -\ \left(0.18\right)^x$

$y=1780\left(.82\right)$

104.

Chloe was studying earthquake waves in Japan. The function of $f\left(x\right)=354\left(1.15\right)^x$ gives the number of waves at the end of x days. What is the growth rate for this function?

a)

The initial number of waves is 15.

b)

The initial number of waves decreases at a rate of 85% each day.

c)

The initial number of waves increases at a rate of 15% each day.

d)

The number of waves at the end of one day is 354.

105.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

106.

This is an example of:

(a)

Choose from the below words

Exponential Growth

Linear Growth

Linear Decay

Exponential Decay

107.

Select all the equations that represent exponential decay.

a)

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

b)

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

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

108.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

e)

I have no idea

109.

Please label each part of the function with the appropriate descricription.

a)

final value

b)

initial value

c)

growth/decay factor

d)

time

1

2

3

4

1)

2)

3)

4)

110.

What is the benefit of starting to invest early, even with a small amount?

a)

Your investments are likely to grow more since compounding means returns get larger over time

b)

You are guaranteed higher returns since compounding reduces the risks of investing

c)

You can use your investments to meet short-term financial goals since you don't need to hold them as long

d)

You can take advantage of brokerage discounts for long-term investors

111.

Emilee has $800 to deposit in an investment account that will triple every year. How much money will Emilee have in 4 years?

(a)

112.

Click on the part of the formula that represents the number of compounding periods per year.

A

B

C

D

E

113.

Click on the part of the formula that represents the time in years since the initial investment.

A

B

C

D

E

114.

What does the model P=A(1+r)^t best represent?

a)

Exponential growth

b)

Simple Interest

c)

Compound Interest

d)

Exponential Decay

115.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

116.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

Chapter 7 Review

Total questions: 116

Worksheet time: 4hrs 55mins

Similar Resources on Wayground