Question 1

Simplify. Write the answer in exponential form without negative exponents.
-$\left( x ^ { - 3 / 5 } \right) ^ { 1 / 7 }$

Accepted Answer

A)  $- x ^ { 35 / 3 }$ 
B)  $\frac { 1 } { x ^ { 3 / 35 } }$ 
C)  $x ^ { 35 / 3 }$ 
D)  $- \frac { 1 } { x ^ { 3 / 35 } }$ 
A)  $- x ^ { 35 / 3 }$ 
B)  $\frac { 1 } { x ^ { 3 / 35 } }$ 
C)  $x ^ { 35 / 3 }$ 
D)  $- \frac { 1 } { x ^ { 3 / 35 } }$

Question 2

Solve the problem.
-A publisher determines that how many books they sell depends on the price of the book. The demand function representing this isrepresenting this is $p = 40 - \sqrt { 0.0001 x + 2 },$ where p represents the price per book in dollars, and x represents the
Number of books sold. If the publisher wants to sell 8,000,000 copies of the book, what price must they charge?

Accepted Answer

A) $30.94 
B) $11.68 
C) $68.32 
D) -$242.85 
A) $30.94 
B) $11.68 
C) $68.32 
D) -$242.85

Question 3

Solve and check your solution(s). If the equation has no real solution, so state.
-$- \sqrt { 4 y + 5 } = - 5$

Accepted Answer

A)  $\frac { 15 } { 2 }$ 
B)  $\frac { 25 } { 4 }$ 
C) 25 
D) 5 
A)  $\frac { 15 } { 2 }$ 
B)  $\frac { 25 } { 4 }$ 
C) 25 
D) 5

Question 4

Simplify by rationalizing the denominator.
-$\frac { 8 } { \sqrt { 2 } + 1 }$

Accepted Answer

A)  $\frac { 8 \sqrt { 2 } + 8 } { 4 }$ 
B)  $8 \sqrt { 2 } - 8$ 
C)  $8 \sqrt { 2 } - 1$ 
D)  $8 \sqrt { 2 } + 8$ 
A)  $\frac { 8 \sqrt { 2 } + 8 } { 4 }$ 
B)  $8 \sqrt { 2 } - 8$ 
C)  $8 \sqrt { 2 } - 1$ 
D)  $8 \sqrt { 2 } + 8$

Question 5

Use absolute value to evaluate.
-$$\sqrt { \left( - \frac { 49 } { 4 } \right) ^ { 2 } }$$

Accepted Answer

A)  $\frac { 7 } { 2 }$ 
B)  $\frac { 49 } { 4 }$ 
C)  $- \frac { 7 } { 2 }$ 
D) not a real number 
A)  $\frac { 7 } { 2 }$ 
B)  $\frac { 49 } { 4 }$ 
C)  $- \frac { 7 } { 2 }$ 
D) not a real number

Question 6

Add or subtract.
-$( 7 + \sqrt { - 2 } ) + ( 5 - \sqrt { - 72 } )$

Accepted Answer

A)  $12 - 5 \mathrm { i } \sqrt { 2 }$ 
B)  $12 + 5 \sqrt { 2 }$ 
C)  $12 - 5 \sqrt { 2 }$ 
D)  $12 + 5 \mathrm { i } \sqrt { 2 }$ 
A)  $12 - 5 \mathrm { i } \sqrt { 2 }$ 
B)  $12 + 5 \sqrt { 2 }$ 
C)  $12 - 5 \sqrt { 2 }$ 
D)  $12 + 5 \mathrm { i } \sqrt { 2 }$

Question 7

Write the expression in exponential form. Assume that all variables represent positive real numbers.
-$\sqrt [ 9 ] { 2 x + 5 y }$

Accepted Answer

A)  $( 2 x + 5 y ) ^ { 1 / 9 }$ 
B)  $\left( \frac { 2 } { 3 } x + \frac { 5 } { 3 } y \right) ^ { 1 / 3 }$ 
C)  $( 2 x + 5 y ) ^ { 1 / 3 }$ 
D)  $( 2 x + 5 y ) ^ { 3 }$ 
A)  $( 2 x + 5 y ) ^ { 1 / 9 }$ 
B)  $\left( \frac { 2 } { 3 } x + \frac { 5 } { 3 } y \right) ^ { 1 / 3 }$ 
C)  $( 2 x + 5 y ) ^ { 1 / 3 }$ 
D)  $( 2 x + 5 y ) ^ { 3 }$

Question 8

Simplify.
-$$\sqrt [ 3 ] { \frac { 7 } { 56 } }$$

Accepted Answer

A)  $\frac { 2 } { \sqrt [ 3 ] { 7 } }$ 
B)  $\frac { \sqrt [ 3 ] { 7 } } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) 2 
A)  $\frac { 2 } { \sqrt [ 3 ] { 7 } }$ 
B)  $\frac { \sqrt [ 3 ] { 7 } } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) 2

Question 9

Simplify by rationalizing the denominator.
-$\frac { 5 } { 6 - \sqrt { x } }$

Accepted Answer

A)  $\frac { 30 + 5 \sqrt { x } } { 36 + x }$ 
B)  $\frac { 5 } { 36 - x }$ 
C)  $\frac { 30 - 5 \sqrt { x } } { 36 - x }$ 
D)  $\frac { 30 + 5 \sqrt { x } } { 36 - x }$ 
A)  $\frac { 30 + 5 \sqrt { x } } { 36 + x }$ 
B)  $\frac { 5 } { 36 - x }$ 
C)  $\frac { 30 - 5 \sqrt { x } } { 36 - x }$ 
D)  $\frac { 30 + 5 \sqrt { x } } { 36 - x }$

Question 10

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.
-$$- \sqrt [ 5 ] { - 243 }$$

Accepted Answer

A) -3 
B) -243 
C) 3 
D) not a real number 
A) -3 
B) -243 
C) 3 
D) not a real number

Question 11

Simplify.
-3 27y - 3 128y

Accepted Answer

A) 4 3 2y - 3 3 y 
B) 7 3 y 
C) 3 3 y - 4 3 2y 
D) 3 - 4 3 2 
A) 4 3 2y - 3 3 y 
B) 7 3 y 
C) 3 3 y - 4 3 2y 
D) 3 - 4 3 2

Question 12

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.
-$$- \sqrt { 58.9 }$$

Accepted Answer

A) -7.66 
B) -7.67 
C) 7.67 
D) not a real number 
A) -7.66 
B) -7.67 
C) 7.67 
D) not a real number

Question 13

Add or subtract.
-$( 12 - i \sqrt { 6 } ) + ( 25 - \sqrt { - 6 } )$

Accepted Answer

A)  $- 13 - 2 i \sqrt { 6 }$ 
B)  $37 - 2 i \sqrt { 6 }$ 
C)  $37 - 2 \sqrt { 6 }$ 
D)  $37 + 2 i \sqrt { 6 }$ 
A)  $- 13 - 2 i \sqrt { 6 }$ 
B)  $37 - 2 i \sqrt { 6 }$ 
C)  $37 - 2 \sqrt { 6 }$ 
D)  $37 + 2 i \sqrt { 6 }$

Question 14

Add or subtract.
-$\left( \frac { 5 } { 2 } - \frac { 7 } { 2 } \mathrm { i } \right) + \left( \frac { 7 } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)$

Accepted Answer

A)  $- 1 + 3 i$ 
B)  $6 - 4 i$ 
C)  $2 + 0 \mathrm { i }$ 
D) 2 + i 
A)  $- 1 + 3 i$ 
B)  $6 - 4 i$ 
C)  $2 + 0 \mathrm { i }$ 
D) 2 + i

Question 15

Add or subtract.
-$( 3.6 - 0.5 \mathrm { i } ) - ( - 5.9 - 5.5 \mathrm { i } )$

Accepted Answer

A)  $3.1 + 11.4 \mathrm { i }$ 
B)  $3.1 - 11.4 \mathrm { i }$ 
C)  $- 2.3 - 6 i$ 
D)  $9.5 + 5 \mathrm { i }$ 
A)  $3.1 + 11.4 \mathrm { i }$ 
B)  $3.1 - 11.4 \mathrm { i }$ 
C)  $- 2.3 - 6 i$ 
D)  $9.5 + 5 \mathrm { i }$

Question 16

Use absolute value to evaluate.
-$$\sqrt [ 5 ] { ( 2 ) ^ { 5 } }$$

Accepted Answer

A) 32 
B) 2 
C) -2 
D) not a real number 
A) 32 
B) 2 
C) -2 
D) not a real number

Question 17

Simplify.
-$\sqrt { 18 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Accepted Answer

A)  $3 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 }$ 
B)  $3 q ^ { 4 } \sqrt { 2 k ^ { 7 } }$ 
C)  $3 k ^ { 7 } q ^ { 8 } \sqrt { 2 k }$ 
D)  $3 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$ 
A)  $3 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 }$ 
B)  $3 q ^ { 4 } \sqrt { 2 k ^ { 7 } }$ 
C)  $3 k ^ { 7 } q ^ { 8 } \sqrt { 2 k }$ 
D)  $3 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$

Question 18

Simplify.
-$\frac { \sqrt { 56 x ^ { 5 } y ^ { 6 } } } { \sqrt { 2 y ^ { 4 } } }$

Accepted Answer

A)  $4 x ^ { 2 } y \sqrt { 7 x }$ 
B)  $2 x ^ { 2 } y \sqrt { 7 x }$ 
C)  $2 x ^ { 4 } y ^ { 2 } \sqrt { 7 x y }$ 
D)  $28 x y \sqrt { x }$ 
A)  $4 x ^ { 2 } y \sqrt { 7 x }$ 
B)  $2 x ^ { 2 } y \sqrt { 7 x }$ 
C)  $2 x ^ { 4 } y ^ { 2 } \sqrt { 7 x y }$ 
D)  $28 x y \sqrt { x }$

Question 19

Simplify the radical expression. Write the answer in radical form when appropriate.
-$\sqrt [ 4 ] { \sqrt [ 5 ] { x y } }$

Accepted Answer

A)  $\sqrt [ 20 ] { x y }$ 
B)  $\sqrt [ 5 ] { x y }$ 
C)  $\sqrt [ 40 ] { x y }$ 
D)  $\sqrt [ 4 ] { x y }$ 
A)  $\sqrt [ 20 ] { x y }$ 
B)  $\sqrt [ 5 ] { x y }$ 
C)  $\sqrt [ 40 ] { x y }$ 
D)  $\sqrt [ 4 ] { x y }$

Question 20

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.
-$$\sqrt [ 4 ] { - \frac { 1 } { 81 } }$$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B) 19 
C)  $- \frac { 1 } { 3 }$ 
D) not a real number 
A)  $\frac { 1 } { 3 }$ 
B) 19 
C)  $- \frac { 1 } { 3 }$ 
D) not a real number

Simplify. Write the answer in exponential form without negative exponents. - $\left( x ^ { - 3 / 5 } \right) ^ { 1 / 7 }$

Solve and check your solution(s). If the equation has no real solution, so state. - $- \sqrt { 4 y + 5 } = - 5$

Simplify by rationalizing the denominator. - $\frac { 8 } { \sqrt { 2 } + 1 }$

Use absolute value to evaluate. - $\sqrt { \left( - \frac { 49 } { 4 } \right) ^ { 2 } }$

Add or subtract. - $( 7 + \sqrt { - 2 } ) + ( 5 - \sqrt { - 72 } )$

Write the expression in exponential form. Assume that all variables represent positive real numbers. - $\sqrt [ 9 ] { 2 x + 5 y }$

Simplify. - $\sqrt [ 3 ] { \frac { 7 } { 56 } }$

Simplify by rationalizing the denominator. - $\frac { 5 } { 6 - \sqrt { x } }$

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $- \sqrt [ 5 ] { - 243 }$

Simplify. -3 27y - 3 128y

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $- \sqrt { 58.9 }$

Add or subtract. - $( 12 - i \sqrt { 6 } ) + ( 25 - \sqrt { - 6 } )$

Add or subtract. - $\left( \frac { 5 } { 2 } - \frac { 7 } { 2 } \mathrm { i } \right) + \left( \frac { 7 } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)$

Add or subtract. - $( 3.6 - 0.5 \mathrm { i } ) - ( - 5.9 - 5.5 \mathrm { i } )$

Use absolute value to evaluate. - $\sqrt [ 5 ] { ( 2 ) ^ { 5 } }$

Simplify. - $\sqrt { 18 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Simplify. - $\frac { \sqrt { 56 x ^ { 5 } y ^ { 6 } } } { \sqrt { 2 y ^ { 4 } } }$

Simplify the radical expression. Write the answer in radical form when appropriate. - $\sqrt [ 4 ] { \sqrt [ 5 ] { x y } }$

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $\sqrt [ 4 ] { - \frac { 1 } { 81 } }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 7: Roots, Radicals, and Complex Numbers

Simplify. Write the answer in exponential form without negative exponents. - (x−3/5)1/7\left( x ^ { - 3 / 5 } \right) ^ { 1 / 7 }(x−3/5)1/7

Solve and check your solution(s). If the equation has no real solution, so state. - −4y+5=−5- \sqrt { 4 y + 5 } = - 5−4y+5​=−5

Simplify by rationalizing the denominator. - 82+1\frac { 8 } { \sqrt { 2 } + 1 }2​+18​

Use absolute value to evaluate. - (−494)2\sqrt { \left( - \frac { 49 } { 4 } \right) ^ { 2 } }(−449​)2​

Add or subtract. - (7+−2)+(5−−72)( 7 + \sqrt { - 2 } ) + ( 5 - \sqrt { - 72 } )(7+−2​)+(5−−72​)

Write the expression in exponential form. Assume that all variables represent positive real numbers. - 2x+5y9\sqrt [ 9 ] { 2 x + 5 y }92x+5y​

Simplify. - 7563\sqrt [ 3 ] { \frac { 7 } { 56 } }3567​​

Simplify by rationalizing the denominator. - 56−x\frac { 5 } { 6 - \sqrt { x } }6−x​5​

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - −−2435- \sqrt [ 5 ] { - 243 }−5−243​