Question 1

Perform the multiplication. The variable represents a positive number. $\sqrt { y } ( \sqrt { 6 y } - 2 )$

Accepted Answer

A)  $y \sqrt { 2 } - 6 \sqrt { y }$ 
B)  $y \sqrt { 6 } + 2 \sqrt { y }$ 
C)  $y \sqrt { 6 } - 2 \sqrt { y }$ 
D)  $6 y - 2 \sqrt { y }$ 
E)  $6 \sqrt { y } - y \sqrt { 2 }$ 
A)  $y \sqrt { 2 } - 6 \sqrt { y }$ 
B)  $y \sqrt { 6 } + 2 \sqrt { y }$ 
C)  $y \sqrt { 6 } - 2 \sqrt { y }$ 
D)  $6 y - 2 \sqrt { y }$ 
E)  $6 \sqrt { y } - y \sqrt { 2 }$

Question 2

Simplify the expression. $\left( 7 x ^ { 8 } \right) ^ { 2 }$

Accepted Answer

A)  $7 x ^ { 16 }$ 
B)  $7 x ^ { 8 }$ 
C)  $49 x ^ { 17 }$ 
D)  $49 x ^ { 16 }$ 
E)  $49 x ^ { 15 }$ 
A)  $7 x ^ { 16 }$ 
B)  $7 x ^ { 8 }$ 
C)  $49 x ^ { 17 }$ 
D)  $49 x ^ { 16 }$ 
E)  $49 x ^ { 15 }$

Question 3

Find the indicated quotient. Express the final result using positive integral exponents only. $$\left( \frac { 63 x ^ { - 2 } y ^ { - 2 } } { 9 x y ^ { 7 } } \right) ^ { - 2 }$$

Accepted Answer

A)  $\frac { 1 } { 49 x ^ { 16 } y ^ { 18 } }$ 
B)  $49 x ^ { 4 } y ^ { 5 }$ 
C)  $49 x ^ { 16 } y ^ { 10 }$ 
D)  $\frac { x ^ { 16 } y ^ { 18 } } { 49 }$ 
E)  $\frac { 49 } { x ^ { 16 } y ^ { 18 } }$ 
A)  $\frac { 1 } { 49 x ^ { 16 } y ^ { 18 } }$ 
B)  $49 x ^ { 4 } y ^ { 5 }$ 
C)  $49 x ^ { 16 } y ^ { 10 }$ 
D)  $\frac { x ^ { 16 } y ^ { 18 } } { 49 }$ 
E)  $\frac { 49 } { x ^ { 16 } y ^ { 18 } }$

Question 4

Simplify the numerical expression. $$\left( 2 ^ { 3 } 3 ^ { - 2 } \right) ^ { - 1 }$$

Accepted Answer

A)  $\frac { 9 } { 8 }$ 
B)  $\frac { 8 } { 9 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 3 }$ 
E)  $\frac { 3 } { 2 }$ 
A)  $\frac { 9 } { 8 }$ 
B)  $\frac { 8 } { 9 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 3 }$ 
E)  $\frac { 3 } { 2 }$

Question 5

Write the number $0.07 \times 10 ^ { 5 }$ in standard notation.

Accepted Answer

A) 7,000,000 
B) 7 
C) 700 
D) 7,000 
E) 70,000 
A) 7,000,000 
B) 7 
C) 700 
D) 7,000 
E) 70,000

Question 6

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous. $\sqrt [ 3 ] { x ^ { 3 } + 1,854 } - 6 = x$

Accepted Answer

A)  $x = 7 , x = - 13$ is extraneous 
B)  $x = 6 , x = - 13$ is extraneous 
C)  $x = 6 , x = - 13$ 
D)  $x = 7 , x = - 5$ 
E)  $x = 7 , x = - 13$ 
A)  $x = 7 , x = - 13$ is extraneous 
B)  $x = 6 , x = - 13$ is extraneous 
C)  $x = 6 , x = - 13$ 
D)  $x = 7 , x = - 5$ 
E)  $x = 7 , x = - 13$

Question 7

Simplify the numerical expression. $$15 ( - 6 ) ^ { 4 } - 3 ( - 5 ) ^ { 3 } + 7 ( - 4 ) + 12$$

Accepted Answer

A) 19,799 
B) 6,593 
C) -16 
D) -331 
E) 65,613,359 
A) 19,799 
B) 6,593 
C) -16 
D) -331 
E) 65,613,359

Question 8

Change the radical to simplest radical form. $\frac { \sqrt { 40 } } { \sqrt { 88 } }$

Accepted Answer

A)  $11 \sqrt { 55 }$ 
B)  $\frac { \sqrt { 55 } } { 11 }$ 
C)  $\frac { 8 \sqrt { 55 } } { 11 }$ 
D)  $\sqrt { \frac { 40 } { 88 } }$ 
E)  $\frac { \sqrt { 55 } } { 88 }$ 
A)  $11 \sqrt { 55 }$ 
B)  $\frac { \sqrt { 55 } } { 11 }$ 
C)  $\frac { 8 \sqrt { 55 } } { 11 }$ 
D)  $\sqrt { \frac { 40 } { 88 } }$ 
E)  $\frac { \sqrt { 55 } } { 88 }$

Question 9

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }$

Accepted Answer

A)  $- \sqrt { 8 }$ 
B)  $\sqrt [ 12 ] { 8 }$ 
C)  $\frac { 1 } { \sqrt [ 12 ] { 8 } \sqrt { 8 } }$ 
D)  $\sqrt [ 7 ] { 8 }$ 
E)  $\sqrt [ 12 ] { 64 }$ 
A)  $- \sqrt { 8 }$ 
B)  $\sqrt [ 12 ] { 8 }$ 
C)  $\frac { 1 } { \sqrt [ 12 ] { 8 } \sqrt { 8 } }$ 
D)  $\sqrt [ 7 ] { 8 }$ 
E)  $\sqrt [ 12 ] { 64 }$

Question 10

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. How far will a car skid if it is going 48 mph on dry pavement? On dry pavement, $k = 5.34$ .

Accepted Answer

A) about 59 ft 
B) about 76 ft 
C) about 99 ft 
D) about 81 ft 
E) about 70 ft 
A) about 59 ft 
B) about 76 ft 
C) about 99 ft 
D) about 81 ft 
E) about 70 ft

Question 11

Express the following as a single fraction involving positive exponents only. $$4 x ^ { - 3 } - 5 x ^ { - 7 }$$

Accepted Answer

A)  $- \frac { 1 } { x ^ { 10 } }$ 
B)  $4 x ^ { 7 } - 5 x ^ { 3 }$ 
C)  $\frac { 4 x ^ { 4 } - 5 } { x ^ { 7 } }$ 
D)  $\frac { 4 x ^ { 4 } - 5 } { x ^ { 6 } }$ 
E)  $\frac { 1 } { 4 x ^ { 7 } - 5 x ^ { 3 } }$ 
A)  $- \frac { 1 } { x ^ { 10 } }$ 
B)  $4 x ^ { 7 } - 5 x ^ { 3 }$ 
C)  $\frac { 4 x ^ { 4 } - 5 } { x ^ { 7 } }$ 
D)  $\frac { 4 x ^ { 4 } - 5 } { x ^ { 6 } }$ 
E)  $\frac { 1 } { 4 x ^ { 7 } - 5 x ^ { 3 } }$

Question 12

Change the radical to simplest radical form. $- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }$

Accepted Answer

A)  $- \frac { \sqrt { 21 } } { 49 }$ 
B)  $\frac { 21 } { 21 } \sqrt { 12 }$ 
C)  $4 \sqrt { 7 }$ 
D)  $- \frac { 4 } { 49 } \sqrt { 7 }$ 
E)  $- \frac { 2 } { 7 } \frac { \sqrt { 4 } } { \sqrt { 7 } }$ 
A)  $- \frac { \sqrt { 21 } } { 49 }$ 
B)  $\frac { 21 } { 21 } \sqrt { 12 }$ 
C)  $4 \sqrt { 7 }$ 
D)  $- \frac { 4 } { 49 } \sqrt { 7 }$ 
E)  $- \frac { 2 } { 7 } \frac { \sqrt { 4 } } { \sqrt { 7 } }$

Question 13

Simplify the expression. $2 ^ { \frac { 4 } { 5 } } 2 ^ { \frac { 6 } { 5 } }$

Accepted Answer

A) 16 
B)  $2 ^ { \frac { 1 } { 5 } }$ 
C) 2 
D) 4 
E) 81 
A) 16 
B)  $2 ^ { \frac { 1 } { 5 } }$ 
C) 2 
D) 4 
E) 81

Question 14

Change the expression into radical notation. $13 ^ { \frac { 1 } { 3 } }$

Accepted Answer

The answer of Change the expression into radical notation. \(13...

Question 15

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. On wet pavement, $k = 3.24$ . How far will a car skid if it is going 51 mph?

Accepted Answer

A) about 225 ft 
B) about 282 ft 
C) about 248 ft 
D) about 203 ft 
E) about 236 ft 
A) about 225 ft 
B) about 282 ft 
C) about 248 ft 
D) about 203 ft 
E) about 236 ft

Question 16

Find a rational approximation, to the nearest tenth, for the radical expression. $2 \sqrt { 5 } + 5 \sqrt { 5 }$

Accepted Answer

A)  $13.8$ 
B)  $19.2$ 
C)  $16.7$ 
D)  $16.8$ 
E)  $15.7$ 
A)  $13.8$ 
B)  $19.2$ 
C)  $16.7$ 
D)  $16.8$ 
E)  $15.7$

Question 17

Multiply and simplify where possible. $\sqrt { 8 } \sqrt { 20 }$

Accepted Answer

A)  $10 \sqrt { 10 }$ 
B)  $2 \sqrt { 10 }$ 
C)  $4 \sqrt { 10 }$ 
D)  $10 \sqrt { 2 }$ 
E)  $8 \sqrt { 10 }$ 
A)  $10 \sqrt { 10 }$ 
B)  $2 \sqrt { 10 }$ 
C)  $4 \sqrt { 10 }$ 
D)  $10 \sqrt { 2 }$ 
E)  $8 \sqrt { 10 }$

Question 18

Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 2 } - \frac { 1 } { 4 } \sqrt { 18 }$

Accepted Answer

A)  $\frac { 12 } { 5 } \sqrt { 2 }$ 
B)  $- \frac { 5 } { 12 } \sqrt { 2 }$ 
C)  $- \frac { 5 } { 12 } \sqrt { 5 }$ 
D)  $\frac { 5 } { 12 } \sqrt { 5 }$ 
E)  $\frac { 5 } { 12 } \sqrt { 2 }$ 
A)  $\frac { 12 } { 5 } \sqrt { 2 }$ 
B)  $- \frac { 5 } { 12 } \sqrt { 2 }$ 
C)  $- \frac { 5 } { 12 } \sqrt { 5 }$ 
D)  $\frac { 5 } { 12 } \sqrt { 5 }$ 
E)  $\frac { 5 } { 12 } \sqrt { 2 }$

Question 19

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.

Accepted Answer

A)  $\sqrt [ 3 ] { 8 }$ 
B)  $\sqrt [ 3 ] { 512 }$ 
C)  $\sqrt [ 4 ] { 8 }$ 
D)  $\sqrt [ 4 ] { 512 }$ 
E)  $\sqrt [ 4 ] { 64 }$ 
A)  $\sqrt [ 3 ] { 8 }$ 
B)  $\sqrt [ 3 ] { 512 }$ 
C)  $\sqrt [ 4 ] { 8 }$ 
D)  $\sqrt [ 4 ] { 512 }$ 
E)  $\sqrt [ 4 ] { 64 }$

Question 20

Simplify the expression. $\left( \frac { 25 } { 36 } \right) ^ { \frac { 3 } { 2 } }$

Accepted Answer

A)  $\frac { 5 } { 6 }$ 
B)  $\frac { 625 } { 1,296 }$ 
C)  $\frac { 125 } { 216 }$ 
D)  $\frac { 216 } { 125 }$ 
E)  $\frac { 126 } { 217 }$ 
A)  $\frac { 5 } { 6 }$ 
B)  $\frac { 625 } { 1,296 }$ 
C)  $\frac { 125 } { 216 }$ 
D)  $\frac { 216 } { 125 }$ 
E)  $\frac { 126 } { 217 }$

Perform the multiplication. The variable represents a positive number. $\sqrt { y } ( \sqrt { 6 y } - 2 )$

Simplify the expression. $\left( 7 x ^ { 8 } \right) ^ { 2 }$

Find the indicated quotient. Express the final result using positive integral exponents only. $\left( \frac { 63 x ^ { - 2 } y ^ { - 2 } } { 9 x y ^ { 7 } } \right) ^ { - 2 }$

Simplify the numerical expression. $\left( 2 ^ { 3 } 3 ^ { - 2 } \right) ^ { - 1 }$

Write the number $0.07 \times 10 ^ { 5 }$ in standard notation.

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous. $\sqrt [ 3 ] { x ^ { 3 } + 1,854 } - 6 = x$

Simplify the numerical expression. $15 ( - 6 ) ^ { 4 } - 3 ( - 5 ) ^ { 3 } + 7 ( - 4 ) + 12$

Change the radical to simplest radical form. $\frac { \sqrt { 40 } } { \sqrt { 88 } }$

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }$

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. How far will a car skid if it is going 48 mph on dry pavement? On dry pavement, $k = 5.34$ .

Express the following as a single fraction involving positive exponents only. $4 x ^ { - 3 } - 5 x ^ { - 7 }$

Change the radical to simplest radical form. $- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }$

Simplify the expression. $2 ^ { \frac { 4 } { 5 } } 2 ^ { \frac { 6 } { 5 } }$

Change the expression into radical notation. $13 ^ { \frac { 1 } { 3 } }$

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. On wet pavement, $k = 3.24$ . How far will a car skid if it is going 51 mph?

Find a rational approximation, to the nearest tenth, for the radical expression. $2 \sqrt { 5 } + 5 \sqrt { 5 }$

Multiply and simplify where possible. $\sqrt { 8 } \sqrt { 20 }$

Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 2 } - \frac { 1 } { 4 } \sqrt { 18 }$

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.

Simplify the expression. $\left( \frac { 25 } { 36 } \right) ^ { \frac { 3 } { 2 } }$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

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Exam 5: Exponents and Radicals

Perform the multiplication. The variable represents a positive number. y(6y−2)\sqrt { y } ( \sqrt { 6 y } - 2 )y​(6y​−2)

Simplify the expression. (7x8)2\left( 7 x ^ { 8 } \right) ^ { 2 }(7x8)2

Find the indicated quotient. Express the final result using positive integral exponents only. (63x−2y−29xy7)−2\left( \frac { 63 x ^ { - 2 } y ^ { - 2 } } { 9 x y ^ { 7 } } \right) ^ { - 2 }(9xy763x−2y−2​)−2

Simplify the numerical expression. (233−2)−1\left( 2 ^ { 3 } 3 ^ { - 2 } \right) ^ { - 1 }(233−2)−1

Write the number 0.07×1050.07 \times 10 ^ { 5 }0.07×105 in standard notation.

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous. x3+1,8543−6=x\sqrt [ 3 ] { x ^ { 3 } + 1,854 } - 6 = x3x3+1,854​−6=x

Simplify the numerical expression. 15(−6)4−3(−5)3+7(−4)+1215 ( - 6 ) ^ { 4 } - 3 ( - 5 ) ^ { 3 } + 7 ( - 4 ) + 1215(−6)4−3(−5)3+7(−4)+12

Change the radical to simplest radical form. 4088\frac { \sqrt { 40 } } { \sqrt { 88 } }88​40​​

Perform the indicated operation and express your answer in simplest radical form. 8384\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }48​38​​

The formula s=kds = k \sqrt { d }s=kd​ relates the speed sss (in mph)of a car and the distance ddd of the skid when a driver hits the brakes. How far will a car skid if it is going 48 mph on dry pavement? On dry pavement, k=5.34k = 5.34k=5.34 .

Express the following as a single fraction involving positive exponents only. 4x−3−5x−74 x ^ { - 3 } - 5 x ^ { - 7 }4x−3−5x−7

Change the radical to simplest radical form. −6122121- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }−2121​612​​

Simplify the expression. 2452652 ^ { \frac { 4 } { 5 } } 2 ^ { \frac { 6 } { 5 } }254​256​

Change the expression into radical notation. 131313 ^ { \frac { 1 } { 3 } }1331​

The formula s=kds = k \sqrt { d }s=kd​ relates the speed sss (in mph)of a car and the distance ddd of the skid when a driver hits the brakes. On wet pavement, k=3.24k = 3.24k=3.24 . How far will a car skid if it is going 51 mph?

Find a rational approximation, to the nearest tenth, for the radical expression. 25+552 \sqrt { 5 } + 5 \sqrt { 5 }25​+55​

Multiply and simplify where possible. 820\sqrt { 8 } \sqrt { 20 }8​20​

Use the distributive property to help simplify the expression. 132−1418\frac { 1 } { 3 } \sqrt { 2 } - \frac { 1 } { 4 } \sqrt { 18 }31​2​−41​18​

Perform the indicated operation and express your answer in simplest radical form. 51248\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }8​4512​​ Express answers in simplest radical form.

Simplify the expression. (2536)32\left( \frac { 25 } { 36 } \right) ^ { \frac { 3 } { 2 } }(3625​)23​

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Perform the multiplication. The variable represents a positive number. $\sqrt { y } ( \sqrt { 6 y } - 2 )$

Simplify the expression. $\left( 7 x ^ { 8 } \right) ^ { 2 }$

Find the indicated quotient. Express the final result using positive integral exponents only. $\left( \frac { 63 x ^ { - 2 } y ^ { - 2 } } { 9 x y ^ { 7 } } \right) ^ { - 2 }$

Simplify the numerical expression. $\left( 2 ^ { 3 } 3 ^ { - 2 } \right) ^ { - 1 }$

Write the number $0.07 \times 10 ^ { 5 }$ in standard notation.

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous. $\sqrt [ 3 ] { x ^ { 3 } + 1,854 } - 6 = x$

Simplify the numerical expression. $15 ( - 6 ) ^ { 4 } - 3 ( - 5 ) ^ { 3 } + 7 ( - 4 ) + 12$

Change the radical to simplest radical form. $\frac { \sqrt { 40 } } { \sqrt { 88 } }$

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }$

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. How far will a car skid if it is going 48 mph on dry pavement? On dry pavement, $k = 5.34$ .

Express the following as a single fraction involving positive exponents only. $4 x ^ { - 3 } - 5 x ^ { - 7 }$

Change the radical to simplest radical form. $- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }$

Simplify the expression. $2 ^ { \frac { 4 } { 5 } } 2 ^ { \frac { 6 } { 5 } }$

Change the expression into radical notation. $13 ^ { \frac { 1 } { 3 } }$

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. On wet pavement, $k = 3.24$ . How far will a car skid if it is going 51 mph?

Find a rational approximation, to the nearest tenth, for the radical expression. $2 \sqrt { 5 } + 5 \sqrt { 5 }$

Multiply and simplify where possible. $\sqrt { 8 } \sqrt { 20 }$

Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 2 } - \frac { 1 } { 4 } \sqrt { 18 }$

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.

Simplify the expression. $\left( \frac { 25 } { 36 } \right) ^ { \frac { 3 } { 2 } }$