Deck 6: Factoring and Applications

Question 1

Choose the one alternative that best completes the statement or answers the question.
Write the expression using exponents.

-7. 7 . 7. 7 . 7 . 7

A) 6⁷
B) 42
C) 7⁶
D) 7⁵

Answer 1

7⁶

Question 2

Choose the one alternative that best completes the statement or answers the question.
Write the expression using exponents.

-x . x . x . x . x . x . x

A) 7^x
B) 7(x)
C) x⁷
D) 7

Answer 2

x⁷

Question 3

Choose the one alternative that best completes the statement or answers the question.
Write the expression using exponents.

-

A)
B) 1
C)
D)

Answer 3

Question 4

Choose the one alternative that best completes the statement or answers the question.
Write the expression using exponents.

-( -2x)( -2x)( -2x)( -2x)

A)
B) -8x
C)
D) -

Question 5

Choose the one alternative that best completes the statement or answers the question.
Write the expression using exponents.

-

A)
B)
C) 6
D)

Question 6

Identify the base and the exponent for the exponential expression.

-( 13x)¹⁵

A) Base: x, exponent: 15
B) Base: 13x, exponent: 15
C) Base: 15, exponent: 13x
D) Base: 15, exponent: x

Question 7

Identify the base and the exponent for the exponential expression.

-8x¹⁰

A) Base: 10, exponent: 8x
B) Base: 10, exponent: x
C) Base: 8x, exponent: 10
D) Base: x, exponent: 10

Question 8

Identify the base and the exponent for the exponential expression.

-8³

A) Base: 8, exponent: 3
B) Base: 3, exponent: 8
C) Base: 24, exponent: 3
D) Base: 3, exponent: 24

Question 9

Identify the base and the exponent for the exponential expression.

--15³

A) Base: 3, exponent: -15
B) Base: 3, exponent: 15
C) Base: 15, exponent: 3
D) Base: -15, exponent: 3

Question 10

Identify the base and the exponent for the exponential expression.

-( -3)¹⁴

A) Base: 14, exponent: -3
B) Base: -3, exponent: 14
C) Base: 3, exponent: 14
D) Base: 14, exponent: 3

Question 11

Identify the base and the exponent for the exponential expression.

--( -13)¹⁰

A) Base: 13, exponent: 10
B) Base: -13, exponent: 10
C) Base: 10, exponent: -13
D) Base: 10, exponent: 13

Question 12

Identify the base and the exponent for the exponential expression.

-y⁷

A) Base: 7, exponent: y
B) Base: 7y, exponent: 7
C) Base: y, exponent: 7
D) Base: 7, exponent: 7y

Question 13

Identify the base and the exponent for the exponential expression.

--y¹¹

A) Base: 11, exponent: y
B) Base: y, exponent: 11
C) Base: 11, exponent: -y
D) Base: -y, exponent: 11

Question 14

Identify the base and the exponent for the exponential expression.

-

A) Base: -3x, exponent: 3
B) Base: x, exponent: 3
C) Base: 3x, exponent: 3
D) Base: 3, exponent: -3x

Question 15

Identify the base and the exponent for the exponential expression.

-

A) Base: 2x, exponent: 5
B) Base: -2x, exponent: 5
C) Base: 5, exponent: -2x
D) Base: x, exponent: 5

Question 16

Evaluate.

-4⁶

A) 24
B) 4096
C) 4 6
D) 5

Question 17

Evaluate.

-

A) -20
B) -100
C) 100
D) 20

Question 18

Evaluate.

-

A) 27
B) -3
C) -27
D) 3

Question 19

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-9⁴ ? 9⁶

A) 81¹⁰
B) 9¹⁰
C) 9²⁴
D) 81²⁴

Question 20

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-( -9)⁷( -9)⁶

A) ( 81)⁴²
B) ( 9)¹³
C) ( 81)¹³
D) ( -9)¹³

Question 21

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-( 3p³)( -2p²)

A) 6p⁶
B) -6p⁶
C) -6p⁵
D) 6p⁵

Question 22

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-7⁸ . 7⁷ .7³

A) 343¹⁶⁸
B) 7¹⁸
C) 343¹⁸
D) 7¹⁶⁸

Question 23

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-m³. m⁹ . m⁶

A) m¹⁵
B) m¹²
C) m³³
D) m¹⁸

Question 24

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-( -7 )( -4 )( 3 )

A) 84
B) 84
C) -84
D) -84

Question 25

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-( -8)( -8)⁴( -8)( -8)( -8)³

A) -8¹⁰
B) ( -8)⁷
C) ( -8)¹⁰
D) ( -8)¹²

Question 26

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

- +

A)
B)
C)
D) The product rule does not apply.

Question 27

Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.

-https://d2lvgg3v3hfg70.cloudfront.net/TB9570/.

A)
B)
C)
D) The product rule does not apply.

Question 28

Use the power rules for exponents to simplify. Write the answer in exponential form.

-

A)
B)
C)
D)

Question 29

Use the power rules for exponents to simplify. Write the answer in exponential form.

-

A)
B)
C)
D)

Question 30

Use the power rules for exponents to simplify. Write the answer in exponential form.

-

A) 45
B)
C) 9
D) t

Question 31

Use the power rules for exponents to simplify. Write the answer in exponential form.

-

A) -
B)
C) -
D)

Question 32

Use the power rules for exponents to simplify. Write the answer in exponential form.

-

A)
B)
C)
D)

Question 33

Use the power rules for exponents to simplify. Write the answer in exponential form.

-8

A)
B) 8t
C) 8
D) 8r

Question 34

Use the power rules for exponents to simplify. Write the answer in exponential form.

-

A) t
B)
C) r
D) 10

Question 35

Use the power rules for exponents to simplify. Write the answer in exponential form.

-

A)
B)
C)
D)

Question 36

Use the power rules for exponents to simplify. Write the answer in exponential form.

- ( v $\neq$ 0)

A)
B)
C)
D)

Question 37

Simplify the expression.

-( -5x⁶y)³

A) ( -5)³x¹⁸y³
B) ( -5)³x⁹y³
C) -15x⁶y³
D) -15x⁶y

Question 38

Simplify the expression.

-( -5p³q³r³)²

A) ( -5)⁶p⁶q⁶r⁶
B) ( -5)²p⁵q⁵r⁵
C) -10p⁵q⁵r⁵
D) ( -5)²p⁶q⁶r⁶

Question 39

Simplify the expression.

- (x?0)

A)
B) x¹¹
C) x²⁸
D)

Question 40

Simplify the expression.

- (q?0)

A)
B)
C)
D)

Question 41

Simplify the expression.

-( -5p)⁸ ( -5p)⁶

A) 5¹⁴p¹⁴
B) 25p¹⁴
C) -5¹⁴p¹⁴
D) 5¹⁴p

Question 42

Simplify the expression.

-( 2p³s⁴)²(s³)

A) 4p⁵s⁹
B) 2p⁶s¹¹
C) 4p⁶s¹¹
D) 4p⁵s²⁴

Question 43

Simplify the expression.

- (s?0)

A)
B)
C)
D)

Question 44

Simplify the expression.

- .

A)
B)
C)
D)

Question 45

Simplify the expression.

-

A) -
B) -
C)
D) -

Question 46

Solve the problem.

-Find an expression that represents the area of the figure.

A) 11
B) 24
C) 24
D) 11

Question 47

Solve the problem.

-Find an expression that represents the area of the figure.

A) 5
B) 10
C) 10
D) 5

Question 48

Solve the problem.

-Find an expression that represents the area of the figure.

A) 16
B) 16
C) 32
D) 32

Question 49

Solve the problem.

-Find an expression that represents the area of the figure.(Leave ? in the answer.)

A) 49 $\pi$
B) 49 $\pi$
C) 14 $\pi$
D) 49 $\pi$

Question 50

Solve the problem.

-Find an expression that represents the volume of the figure.

A) 96
B) 12
C) 64
D) 64

Question 51

Solve the problem.

-Find an expression that represents the volume of the figure.

A) 14
B) 84
C) 84
D) 84

Question 52

Solve the problem.

-Find an expression that represents the volume of the figure.

A) 60
B) 60
C) 60
D) 120

Question 53

The formula for compound interest is where A is the amount accumulated from a principal of P dollars left untouched for n years with an annual interest rate r (expressed as a decimal). Use this formula and a calculator to find A to the nearest cent.

-P = $50, r = 0.10, n = 3

A) $166.55
B) $66.55
C) $165.00
D) $166,375.00

Question 54

The formula for compound interest is where A is the amount accumulated from a principal of P dollars left untouched for n years with an annual interest rate r (expressed as a decimal). Use this formula and a calculator to find A to the nearest cent.

-P = $100, r = 0.03, n = 6

A) $1,194,052,296,529.00
B) $69.41
C) $119.41
D) $169.41

Question 55

Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.
-Explain how ( -4)⁷ and -4⁷ are different.

Question 56

Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.
-Explain how ( -8x)⁸ and -8x⁸ are different.

Question 57

Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.
-Does the product rule apply to 3⁶ ∙ 5⁷? Explain why or why not.

Question 58

Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.
-Is ( 5x⁵y¹⁰)² equivalent to 10x¹⁰y²⁰?

Question 59

Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.
-Is it correct to simplify 4² ∙ 2⁴ as 8⁸?

Question 60

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-3⁰

A) 1
B) -1
C) 3
D) 0

Question 61

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

--11⁰

A) -1
B) -11
C) 0
D) 1

Question 62

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-

A) 1
B) ^-1
C) 9
D) 0

Question 63

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

- -

A) ¹
B) 0
C) -1
D) 2

Question 64

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-

A) 1
B) -6
C) 0
D) ^-1

Question 65

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-6⁰ + 5⁰

A) 0
B) 11
C) 1
D) 2

Question 66

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-12⁰ - 2⁰

A) 10
B) 0
C) 2
D) 1

Question 67

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-6⁰ + ( -3)⁰

A) 2
B) 0
C) 3
D) 1

Question 68

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

--( 9⁰) + ( -13)⁰

A) 1
B) 0
C) -4
D) -2

Question 69

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-( -4)⁰ + ( -15)⁰

A) 0
B) -19
C) 2
D) -2

Question 70

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-4^-3

A) -64
B)
C)
D) 64

Question 71

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-

A) 125
B)
C) -125
D)

Question 72

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-( -4)^-2

A) 16
B)
C) -
D) -16

Question 73

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-

A) - 27
B)
C) 27
D) -

Question 74

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

--3^-4

A) -
B) 81
C) -81
D)

Question 75

Choose the one alternative that best completes the statement or answers the question.Evaluate the expression.

-9^-1 + 2^-1

A)
B)
C)
D) 2

Question 76

Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers

-

A) 2¹²
B) 2²
C)
D) 2⁸

Question 77

Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers

-

A)
B) y¹³
C)
D)

Question 78

Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers

-

A)
B)
C) 1
D)

Question 79

Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers

-

A)
B)
C)
D)

Question 80

Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers

-

A)
B)
C)
D)