Deck 9: Rational Exponents

Question 1

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

A)
B)
C)
D)
E)

Answer 1

E

Question 2

Use the definition of rational exponents to write the following with the appropriate root. Then simplify.

A)
B)
C)
D)
E)

Answer 2

C

Question 3

Find the following root, if possible.

A) - 11
B) - 12
C) 13
D) 11
E) Not a real number

Answer 3

A

Question 4

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

A)
B)
C)
D)
E) none of these

Question 5

Use the rational exponent theorem to simplify the following as much as possible.

A)
B)
C)
D)
E)

Question 6

Find the following root, if possible.

A) 9
B) -7
C) - 9
D) - 40.5
E) Not a real number

Question 7

The maximum speed ( v ) that an automobile can travel around a curve of radius r without skidding is given by the equation where v is in miles per hour and r is measured in feet. What is the maximum speed a car can travel around a curve with a radius of 360 feet without skidding?

A) The maximum speed is 180 mph.
B) The maximum speed is 25 mph.
C) The maximum speed is 12 mph.
D) The maximum speed is 90 mph.
E) The maximum speed is 30 mph.

Question 8

Simplify the expression. Remember, negative exponents give reciprocals.

A)
B)
C)
D)
E)

Question 9

Use the definition of rational exponents to write the following with the appropriate root. Then simplify.

A)
B)
C)
D)
E)

Question 10

Simplify the expression. Remember, negative exponents give reciprocals.

A)
B)
C)
D)
E)

Question 11

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

A)
B)
C)
D)
E)

Question 12

Use the definition of rational exponents to write the following with the appropriate root. Then simplify.

A) 2
B) 3
C) - 4
D) - 2
E) not a real number

Question 13

Find the following root, if possible.

A) 0.64
B) 0.3
C) 0.16
D) 0.4
E) Not a real number

Question 14

Use the definition of rational exponents to write the following with the appropriate root. Then simplify.

Question 15

The time t in seconds it takes an object to fall d feet is given by the following equation. An object took 40 seconds to fall to the ground. From what distance must it have been dropped?

A) It have been dropped from 12,800 feet.
B) It have been dropped from 25,600 feet.
C) It have been dropped from 640 feet.
D) It have been dropped from 51,200 feet.
E) It have been dropped from 6,400 feet.

Question 16

Simplify the expression. Remember, negative exponents give reciprocals.

A)
B)
C)
D)
E)

Question 17

Simplify the expression. Assume all variables represent nonnegative numbers.

A)
B)
C)
D)
E)

Question 18

Simplify the expression. Assume all variables represent nonnegative numbers.

A)
B)
C)
D)
E)

Question 19

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

A)
B)
C)
D)
E)

Question 20

Find the following root, if possible.

A) 4
B) 7
C) - 4
D) - 16
E) Not a real number

Question 21

Use the rational exponent theorem to simplify the following as much as possible.

Question 22

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

Question 23

Simplify the expression. Assume all variables represent nonnegative numbers.

Question 24

Find the following root, if possible. If impossible, write not a real number.

Question 25

Find the following root, if possible.

Question 26

Simplify the expression. Remember, negative exponents give reciprocals.

Question 27

Find the following root, if possible.

Question 28

The maximum speed ( v ) that an automobile can travel around a curve of radius r without skidding is given by the equation where v is in miles per hour and r is measured in feet. What is the maximum speed a car can travel around a curve with a radius of 490 feet without skidding? __________ mph

Question 29

The time t in seconds it takes an object to fall d feet is given by the following equation. An object took 25 seconds to fall to the ground. From what distance must it have been dropped? __________ feet

Question 30

Find the following root, if possible.

Question 31

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

Question 32

Simplify the expression. Remember, negative exponents give reciprocals.

Question 33

Multiply. (Assume the variable represents a nonnegative real number.)

A)
B)
C)
D)
E)

Question 34

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

Question 35

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

Question 36

Use the definition of rational exponents to write the following with the appropriate root. Then simplify.

Question 37

Simplify the expression. Assume all variables represent nonnegative numbers.

Question 38

Use the definition of rational exponents to write the following with the appropriate root. Then simplify.

Question 39

Multiply. (Assume the variable represents a nonnegative real number.)

A)
B)
C)
D)
E)

Question 40

Simplify the expression. Remember, negative exponents give reciprocals.

Question 41

Multiply. (Assume the variable represents a nonnegative real number.)

A)
B)
C)
D)
E)

Question 42

Factor the expression as if it were a trinomial.

A)
B)
C)
D)
E)

Question 43

Divide.

A)
B)
C)
D)
E)

Question 44

Simplify the expression to a single fraction.

Question 45

Multiply. (Assume the variables represent nonnegative real numbers.)

A)
B)
C)
D)

Question 46

Multiply. (Assume the variables represent nonnegative real numbers.)

A)
B)
C)
D)
E)

Question 47

Multiply. (Assume the variable represents a nonnegative real number.)

A)
B)
C)
D)
E)

Question 48

Multiply. (Assume the variables represent nonnegative real numbers.)

A)
B)
C)
D)
E)

Question 49

Factor the expression as if it were a trinomial.

A)
B)
C)
D)
E) none of these

Question 50

Factor from

A)
B)
C)
D)
E)

Question 51

Simplify the expression to a single fraction.

A)
B)
C)
D)
E)

Question 52

Simplify the expression to a single fraction.

Question 53

Multiply. (Assume the variable represents a nonnegative real number.)

A)
B)
C)
D)
E)

Question 54

Multiply. (Assume the variable represents a nonnegative real number.)

A)
B)
C)
D)
E)

Question 55

Multiply. (Assume the variables represent nonnegative real numbers.)

A)
B)
C)
D)
E)

Question 56

Factor the expression as if it were a trinomial.

A)
B)
C)
D)
E)

Question 57

Multiply. (Assume the variables represent nonnegative real numbers.)

A)
B)
C)
D)
E)

Question 58

Factor from

A)
B)
C)
D)
E)

Question 59

Simplify the expression to a single fraction.

A)
B)
C)
D)
E)

Question 60

Divide.

A)
B)
C)
D)
E)

Question 61

Multiply. (Assume the variables represent nonnegative real numbers.)

Question 62

Simplify the expression. Do not assume that the variables represent positive numbers.

A)
B)
C)
D)
E)

Question 63

Multiply. (Assume the variables represent nonnegative real numbers.)

Question 64

Multiply. (Assume the variable represents a nonnegative real number.)

Question 65

Multiply. (Assume the variable represents a nonnegative real number.)

Question 66

Multiply. (Assume the variable represents a nonnegative real number.)

Question 67

Multiply. (Assume the variables represent nonnegative real numbers.)

Question 68

Multiply. (Assume the variable represents a nonnegative real number.)

Question 69

Factor from

Question 70

Factor the expression as if it were a trinomial.

Question 71

Multiply. (Assume the variables represent nonnegative real numbers.)

Question 72

Factor the expression as if it were a trinomial.

Question 73

Divide.

Question 74

Use Property 1 for Radicals to write the expression in simplified form.

A)
B)
C)
D)
E)

Question 75

Multiply. (Assume the variable represents a nonnegative real number.)

Question 76

Factor from

Question 77

Multiply. (Assume the variable represents a nonnegative real number.)

Question 78

Multiply. (Assume the variables represent nonnegative real numbers.)

Question 79

Factor the expression as if it were a trinomial.

Question 80

Divide.