Question 1

Simplify the expression below. $\left( 4 x ^ { 6 } y ^ { 6 } \right) ^ { 1 / 2 }$

Accepted Answer

A)  $4 x ^ { 2 } y ^ { 3 }$ 
B)  $2 x ^ { 6 } y ^ { 6 }$ 
C)  $4 x ^ { 3 } y ^ { 3 }$ 
D)  $2 x ^ { 2 } y ^ { 3 }$ 
E)  $2 x ^ { 3 } y ^ { 3 }$ 
A)  $4 x ^ { 2 } y ^ { 3 }$ 
B)  $2 x ^ { 6 } y ^ { 6 }$ 
C)  $4 x ^ { 3 } y ^ { 3 }$ 
D)  $2 x ^ { 2 } y ^ { 3 }$ 
E)  $2 x ^ { 3 } y ^ { 3 }$ E

Question 2

Evaluate $3 r ^ { 3 } s ^ { 2 }$ when $r = 2$ and $s = 3.$

Accepted Answer

A) 216 
B) 18 
C) 324 
D) 5832 
E) 72 
A) 216 
B) 18 
C) 324 
D) 5832 
E) 72 A

Question 3

Simplify the complex fraction. $\frac { \left( \sqrt { 5 x } - \frac { 1 } { 8 \sqrt { 5 x } } \right) } { \sqrt { 5 x } }$

Accepted Answer

A)  $- \frac { 1 } { 8 \sqrt { 5 x } }$ 
B)  $\frac { 40 x - 1 } { 40 x } , x > 0$ 
C)  $\frac { \sqrt { 5 x } - 1 } { 40 x }$ 
D)  $\frac { 8 \sqrt { 5 x } - 1 } { 40 x }$ 
E)  $- \frac { \sqrt { 5 x } } { 40 x }$ 
A)  $- \frac { 1 } { 8 \sqrt { 5 x } }$ 
B)  $\frac { 40 x - 1 } { 40 x } , x > 0$ 
C)  $\frac { \sqrt { 5 x } - 1 } { 40 x }$ 
D)  $\frac { 8 \sqrt { 5 x } - 1 } { 40 x }$ 
E)  $- \frac { \sqrt { 5 x } } { 40 x }$ B

Question 4

Evaluate the expression for the given value of x. $3 x ^ { 3 }$ x = -2

Accepted Answer

A) -18 
B)  $\frac { 1 } { 24 }$ 
C)  $- \frac { 1 } { 24 }$ 
D) -24 
E) 24 
A) -18 
B)  $\frac { 1 } { 24 }$ 
C)  $- \frac { 1 } { 24 }$ 
D) -24 
E) 24

Question 5

When food is placed in a refrigerator, the time required for the food to cool depends on the amount of food, the air circulation in the refrigerator, the original temperature of the food, and the temperature of the refrigerator. One model for the temperature of food that starts at $75 ^ { \circ } F$ and is placed in a $40 ^ { \circ } F$ refrigerator is $T = 10 \left( \frac { 4 t ^ { 2 } + 16 t + 75 } { t ^ { 2 } + 4 t + 10 } \right),$ $t \geq 0$ where $T$ is the temperature (in degrees Fahrenheit) and $t$ is the time (in hours). According to the model, after how many hours will the food reach a temperature of $66 ^ { \circ } \mathrm { F } ?$

Accepted Answer

A) after 4 hours 
B) after 1 hour 
C) after 3 hours 
D) after 5 hours 
E) after 2 hours 
A) after 4 hours 
B) after 1 hour 
C) after 3 hours 
D) after 5 hours 
E) after 2 hours

Question 6

A stream of water moving at a rate of $v$ feet per second can carry particles of size $0.03 \sqrt { v }$ inches. Find the size of the largest particle that can be carried by a stream flowing at the rate of $\frac { 3 } { 5 }$ foot per second. Round to the nearest thousandth of an inch.

Accepted Answer

A) 0.019 inch 
B) 0.023 inch 
C) 0.021 inch 
D) 0.016 inch 
E) 0.028 inch 
A) 0.019 inch 
B) 0.023 inch 
C) 0.021 inch 
D) 0.016 inch 
E) 0.028 inch

Question 7

Simplify the radical expression. $\sqrt [ 4 ] { 243 n ^ { 19 } t ^ { - 20 } }$

Accepted Answer

A)  $\frac { 3 n \sqrt [ 4 ] { 3 n ^ { 15 } } } { t \sqrt { t ^ { 16 } } }$ 
B)  $\frac { 3 n ^ { 4 } \sqrt [ 4 ] { 3 n ^ { 3 } } } { t ^ { 5 } }$ 
C)  $\frac { 3 n \sqrt [ 4 ] { 3 n ^ { 3 } } } { t }$ 
D)  $\frac { 81 n ^ { 16 } \sqrt [ 4 ] { 3 n ^ { 3 } } } { t ^ { 20 } }$ 
E)  $\frac { 81 n \sqrt [ 4 ] { 3 n ^ { 15 } } } { t \sqrt { t ^ { 16 } } }$ 
A)  $\frac { 3 n \sqrt [ 4 ] { 3 n ^ { 15 } } } { t \sqrt { t ^ { 16 } } }$ 
B)  $\frac { 3 n ^ { 4 } \sqrt [ 4 ] { 3 n ^ { 3 } } } { t ^ { 5 } }$ 
C)  $\frac { 3 n \sqrt [ 4 ] { 3 n ^ { 3 } } } { t }$ 
D)  $\frac { 81 n ^ { 16 } \sqrt [ 4 ] { 3 n ^ { 3 } } } { t ^ { 20 } }$ 
E)  $\frac { 81 n \sqrt [ 4 ] { 3 n ^ { 15 } } } { t \sqrt { t ^ { 16 } } }$

Question 8

Determine which numbers in the set are integers. $0.77,4 , - 8 \pi , 0,6.0 , - 8$

Accepted Answer

A)  $4,0,6.0 , - 8$ 
B)  $0.77,4,0,6.0 , - 8$ 
C)  $4,0$ 
D)  $4 , - 8 \pi , 0 , - 8$ 
E)  $4,0 , - 8$ 
A)  $4,0,6.0 , - 8$ 
B)  $0.77,4,0,6.0 , - 8$ 
C)  $4,0$ 
D)  $4 , - 8 \pi , 0 , - 8$ 
E)  $4,0 , - 8$

Question 9

Evaluate the expression for the given value of x. $8 x ^ { - 3 }$ x = 5

Accepted Answer

A)  $\frac { 8 } { 125 }$ 
B)  $- \frac { 8 } { 125 }$ 
C)  $- \frac { 1 } { 120 }$ 
D) 120 
E) -120 
A)  $\frac { 8 } { 125 }$ 
B)  $- \frac { 8 } { 125 }$ 
C)  $- \frac { 1 } { 120 }$ 
D) 120 
E) -120

Question 10

Evaluate the expression for the given value of x. $- 4 x ^ { 0 }$ x = 5

Accepted Answer

A) 0 
B) -4 
C) 4 
D) 20 
E) -20 
A) 0 
B) -4 
C) 4 
D) 20 
E) -20

Question 11

Find the special product. (-4x + 5)(-4x - 5)

Accepted Answer

A) -8x 
B) -8x2 
C) 16x2 - 25 
D) 16x2 + 25 
E) 16x2 - 40x - 25 
A) -8x 
B) -8x2 
C) 16x2 - 25 
D) 16x2 + 25 
E) 16x2 - 40x - 25

Question 12

Write the following number in scientific notation. 22,100,000

Accepted Answer

A)  $2.21 \times 10 ^ { 5 }$ 
B)  $2.21 \times 10 ^ { 6 }$ 
C)  $2.21 \times 10 ^ { 7 }$ 
D)  $2.21 \times 10 ^ { - 7 }$ 
E)  $2.21 \times 10 ^ { - 5 }$ 
A)  $2.21 \times 10 ^ { 5 }$ 
B)  $2.21 \times 10 ^ { 6 }$ 
C)  $2.21 \times 10 ^ { 7 }$ 
D)  $2.21 \times 10 ^ { - 7 }$ 
E)  $2.21 \times 10 ^ { - 5 }$

Question 13

Simplify the following radical expression. $\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }$

Accepted Answer

A)  $4 p q \sqrt [ 3 ] { 6 p q ^ { 2 } }$ 
B)  $4 p ^ { 3 } q ^ { 2 } \sqrt [ 3 ] { 6 q }$ 
C)  $6 p q ^ { 2 } \sqrt [ 3 ] { 4 p q }$ 
D)  $4 \sqrt [ 3 ] { 6 p q ^ { 2 } }$ 
E)  $4 p ^ { 2 } q \sqrt [ 3 ] { 6 p q }$ 
A)  $4 p q \sqrt [ 3 ] { 6 p q ^ { 2 } }$ 
B)  $4 p ^ { 3 } q ^ { 2 } \sqrt [ 3 ] { 6 q }$ 
C)  $6 p q ^ { 2 } \sqrt [ 3 ] { 4 p q }$ 
D)  $4 \sqrt [ 3 ] { 6 p q ^ { 2 } }$ 
E)  $4 p ^ { 2 } q \sqrt [ 3 ] { 6 p q }$

Question 14

Identify the rules of algebra illustrated from left to right by the following statement. $\frac { 1 } { 3 } ( 3 t ) = \left( \frac { 1 } { 3 } \cdot 3 \right) t = 1 \cdot t = t$

Accepted Answer

A) associative property of multiplication; multiplicative inverse property; multiplicative identity property 
B) commutative property of multiplication; multiplicative inverse property; multiplicative identity property 
C) associative property of multiplication; multiplicative identity property; multiplicative inverse property 
D) commutative property of multiplication; multiplicative identity property; multiplicative inverse property 
E) distributive property; multiplicative identity property; multiplicative inverse property 
A) associative property of multiplication; multiplicative inverse property; multiplicative identity property 
B) commutative property of multiplication; multiplicative inverse property; multiplicative identity property 
C) associative property of multiplication; multiplicative identity property; multiplicative inverse property 
D) commutative property of multiplication; multiplicative identity property; multiplicative inverse property 
E) distributive property; multiplicative identity property; multiplicative inverse property

Question 15

Reduce the index of the radical. $\sqrt [ 9 ] { y ^ { 15 } }$

Accepted Answer

A)  $y ^ { 6 }$ 
B)  $\frac { 1 } { y ^ { 6 } }$ 
C)  $\sqrt [ 3 ] { y ^ { 5 } }$ 
D)  $\sqrt [ 6 ] { y }$ 
E)  $\sqrt { y ^ { 6 } }$ 
A)  $y ^ { 6 }$ 
B)  $\frac { 1 } { y ^ { 6 } }$ 
C)  $\sqrt [ 3 ] { y ^ { 5 } }$ 
D)  $\sqrt [ 6 ] { y }$ 
E)  $\sqrt { y ^ { 6 } }$

Question 16

Write the polynomial in standard form.
-6 + 4x2 + 2x

Accepted Answer

The answer of Write the polynomial in standard form.
-6 +...

Question 17

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\sqrt [ 4 ] { 8 }$

Accepted Answer

A) 1.682 
B) 32.000 
C) 2.828 
D) 2.000 
E) 12.000 
A) 1.682 
B) 32.000 
C) 2.828 
D) 2.000 
E) 12.000

Question 18

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 16 } { \sqrt [ 3 ] { 4 } }$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 4 }$ 
B)  $4 \sqrt [ 3 ] { 16 }$ 
C)  $4 \sqrt { 4 }$ 
D)  $16 \sqrt [ 3 ] { 4 }$ 
E)  $4$ 
A)  $4 \sqrt [ 3 ] { 4 }$ 
B)  $4 \sqrt [ 3 ] { 16 }$ 
C)  $4 \sqrt { 4 }$ 
D)  $16 \sqrt [ 3 ] { 4 }$ 
E)  $4$

Question 19

Rationalize the denominator. Then simplify your answer. $\frac { 15 } { \sqrt { 33 } }$

Accepted Answer

A)  $\frac { 75 } { 11 }$ 
B)  $\frac { 10 } { 11 }$ 
C)  $\frac { 5 \sqrt { 33 } } { 11 }$ 
D)  $\frac { \sqrt { 495 } } { 33 }$ 
E)  $\frac { 2 \sqrt { 12 } } { 33 }$ 
A)  $\frac { 75 } { 11 }$ 
B)  $\frac { 10 } { 11 }$ 
C)  $\frac { 5 \sqrt { 33 } } { 11 }$ 
D)  $\frac { \sqrt { 495 } } { 33 }$ 
E)  $\frac { 2 \sqrt { 12 } } { 33 }$

Question 20

Simplify the expression below. $2 ^ { 1 / 3 } \cdot 2 ^ { 11 / 3 }$

Accepted Answer

A)  $8$ 
B)  $16$ 
C)  $32$ 
D)  $256$ 
E)  $16 \sqrt [ 3 ] { 2 }$ 
A)  $8$ 
B)  $16$ 
C)  $32$ 
D)  $256$ 
E)  $16 \sqrt [ 3 ] { 2 }$

Simplify the expression below. $\left( 4 x ^ { 6 } y ^ { 6 } \right) ^ { 1 / 2 }$

Evaluate $3 r ^ { 3 } s ^ { 2 }$ when $r = 2$ and $s = 3.$

Simplify the complex fraction. $\frac { \left( \sqrt { 5 x } - \frac { 1 } { 8 \sqrt { 5 x } } \right) } { \sqrt { 5 x } }$

Evaluate the expression for the given value of x. $3 x ^ { 3 }$ x = -2

A stream of water moving at a rate of $v$ feet per second can carry particles of size $0.03 \sqrt { v }$ inches. Find the size of the largest particle that can be carried by a stream flowing at the rate of $\frac { 3 } { 5 }$ foot per second. Round to the nearest thousandth of an inch.

Simplify the radical expression. $\sqrt [ 4 ] { 243 n ^ { 19 } t ^ { - 20 } }$

Determine which numbers in the set are integers. $0.77,4 , - 8 \pi , 0,6.0 , - 8$

Evaluate the expression for the given value of x. $8 x ^ { - 3 }$ x = 5

Evaluate the expression for the given value of x. $- 4 x ^ { 0 }$ x = 5

Find the special product. (-4x + 5)(-4x - 5)

Write the following number in scientific notation. 22,100,000

Simplify the following radical expression. $\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }$

Identify the rules of algebra illustrated from left to right by the following statement. $\frac { 1 } { 3 } ( 3 t ) = \left( \frac { 1 } { 3 } \cdot 3 \right) t = 1 \cdot t = t$

Reduce the index of the radical. $\sqrt [ 9 ] { y ^ { 15 } }$

Write the polynomial in standard form. -6 + 4x2 + 2x

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\sqrt [ 4 ] { 8 }$

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 16 } { \sqrt [ 3 ] { 4 } }$

Rationalize the denominator. Then simplify your answer. $\frac { 15 } { \sqrt { 33 } }$

Simplify the expression below. $2 ^ { 1 / 3 } \cdot 2 ^ { 11 / 3 }$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Exam 1: Fundamental Concepts of Algebra

Simplify the expression below. (4x6y6)1/2\left( 4 x ^ { 6 } y ^ { 6 } \right) ^ { 1 / 2 }(4x6y6)1/2

Evaluate 3r3s23 r ^ { 3 } s ^ { 2 }3r3s2 when r=2r = 2r=2 and s=3.s = 3.s=3.

Simplify the complex fraction. (5x−185x)5x\frac { \left( \sqrt { 5 x } - \frac { 1 } { 8 \sqrt { 5 x } } \right) } { \sqrt { 5 x } }5x​(5x​−85x​1​)​

Evaluate the expression for the given value of x. 3x33 x ^ { 3 }3x3 x = -2

Simplify the radical expression. 243n19t−204\sqrt [ 4 ] { 243 n ^ { 19 } t ^ { - 20 } }4243n19t−20​

Determine which numbers in the set are integers. 0.77,4,−8π,0,6.0,−80.77,4 , - 8 \pi , 0,6.0 , - 80.77,4,−8π,0,6.0,−8

Evaluate the expression for the given value of x. 8x−38 x ^ { - 3 }8x−3 x = 5

Evaluate the expression for the given value of x. −4x0- 4 x ^ { 0 }−4x0 x = 5

Find the special product. (-4x + 5)(-4x - 5)

Write the following number in scientific notation. 22,100,000

Simplify the following radical expression. 384p4q53\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }3384p4q5​

Identify the rules of algebra illustrated from left to right by the following statement. 13(3t)=(13⋅3)t=1⋅t=t\frac { 1 } { 3 } ( 3 t ) = \left( \frac { 1 } { 3 } \cdot 3 \right) t = 1 \cdot t = t31​(3t)=(31​⋅3)t=1⋅t=t

Reduce the index of the radical. y159\sqrt [ 9 ] { y ^ { 15 } }9y15​

Write the polynomial in standard form. -6 + 4x2 + 2x

Use a calculator to approximate the number. (Round your answer to three decimal places.) 84\sqrt [ 4 ] { 8 }48​

Rewrite the expression below by rationalizing the denominator. Simplify your answer. 1643\frac { 16 } { \sqrt [ 3 ] { 4 } }34​16​

Rationalize the denominator. Then simplify your answer. 1533\frac { 15 } { \sqrt { 33 } }33​15​

Simplify the expression below. 21/3⋅211/32 ^ { 1 / 3 } \cdot 2 ^ { 11 / 3 }21/3⋅211/3

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Simplify the expression below. $\left( 4 x ^ { 6 } y ^ { 6 } \right) ^ { 1 / 2 }$

Evaluate $3 r ^ { 3 } s ^ { 2 }$ when $r = 2$ and $s = 3.$

Simplify the complex fraction. $\frac { \left( \sqrt { 5 x } - \frac { 1 } { 8 \sqrt { 5 x } } \right) } { \sqrt { 5 x } }$

Evaluate the expression for the given value of x. $3 x ^ { 3 }$ x = -2

Simplify the radical expression. $\sqrt [ 4 ] { 243 n ^ { 19 } t ^ { - 20 } }$

Determine which numbers in the set are integers. $0.77,4 , - 8 \pi , 0,6.0 , - 8$

Evaluate the expression for the given value of x. $8 x ^ { - 3 }$ x = 5

Evaluate the expression for the given value of x. $- 4 x ^ { 0 }$ x = 5

Simplify the following radical expression. $\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }$

Identify the rules of algebra illustrated from left to right by the following statement. $\frac { 1 } { 3 } ( 3 t ) = \left( \frac { 1 } { 3 } \cdot 3 \right) t = 1 \cdot t = t$

Reduce the index of the radical. $\sqrt [ 9 ] { y ^ { 15 } }$

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\sqrt [ 4 ] { 8 }$

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 16 } { \sqrt [ 3 ] { 4 } }$

Rationalize the denominator. Then simplify your answer. $\frac { 15 } { \sqrt { 33 } }$

Simplify the expression below. $2 ^ { 1 / 3 } \cdot 2 ^ { 11 / 3 }$