Question 1

Simplify the expression. Express final results without using zero or negative integers as exponents. ( 3 x 4 y -5 ) -4

Accepted Answer

A)  $\frac { y ^ { 20 } } { 81 x ^ { 16 } }$ 
B)  $\frac { 81 x ^ { 16 } } { y ^ { 20 } }$ 
C)  $81 y ^ { 20 } x ^ { 16 }$ 
A)  $\frac { y ^ { 20 } } { 81 x ^ { 16 } }$ 
B)  $\frac { 81 x ^ { 16 } } { y ^ { 20 } }$ 
C)  $81 y ^ { 20 } x ^ { 16 }$

Question 2

Solve the equation. $\sqrt { n + 9 } = n + 9$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(\sqrt { n +...

Question 3

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { 5 } { \sqrt { b } + 4 }$ Please enter your answer as a fraction.

Accepted Answer

The answer of Rationalize the denominator and simplify. All variables...

Question 4

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement.
-$54,880 \sqrt [ 3 ] { 3 }$

Accepted Answer

A)  $( 14 \sqrt [ 3 ] { 196 } ) ( 20 \sqrt [ 3 ] { 14 } )$ 
B)  $( 196 \sqrt [ 3 ] { 3 } ) ( 20 \sqrt [ 3 ] { 9 } )$ 
C)  $( 196 \sqrt [ 3 ] { 42 } ) ( 20 \sqrt [ 3 ] { 196 } )$ 
D)  $( 9 \sqrt [ 3 ] { 42 } ) ( 14 \sqrt [ 3 ] { 9 } )$ 
A)  $( 14 \sqrt [ 3 ] { 196 } ) ( 20 \sqrt [ 3 ] { 14 } )$ 
B)  $( 196 \sqrt [ 3 ] { 3 } ) ( 20 \sqrt [ 3 ] { 9 } )$ 
C)  $( 196 \sqrt [ 3 ] { 42 } ) ( 20 \sqrt [ 3 ] { 196 } )$ 
D)  $( 9 \sqrt [ 3 ] { 42 } ) ( 14 \sqrt [ 3 ] { 9 } )$

Question 5

If b is a nonzero real number, then $b ^ { 0 } = 0$ .

Accepted Answer

A) True 
 B)False

Question 6

Simplify the expression. Express final results without using zero or negative integers as exponents. a 4 a -7 a -2

Accepted Answer

A)  $a ^ { 5 }$ 
B)  $\frac { 1 } { a ^ { 5 } }$ 
C)  $\frac { 1 } { a ^ { 6 } }$ 
A)  $a ^ { 5 }$ 
B)  $\frac { 1 } { a ^ { 5 } }$ 
C)  $\frac { 1 } { a ^ { 6 } }$

Question 7

Solve the equation. $\sqrt { 5 y - 29 } - 3 = 0$

Accepted Answer

A)  y = 4 
B)  y = 5 
C)  y = 8 
A)  y = 4 
B)  y = 5 
C)  y = 8

Question 8

Simplify. Express final results using positive exponents only. $\frac { 28 b ^ { \frac { 1 } { 7 } } } { 7 b ^ { \frac { 8 } { 7 } } }$

Accepted Answer

A)  $\frac { 4 } { b }$ 
B)  $\frac { 4 } { b ^ { \frac { 8 } { 7 } } }$ 
C)  $\frac { b } { 4 }$ 
D)  $\left( \frac { 4 } { b } \right) ^ { \frac { 8 } { 7 } }$ 
A)  $\frac { 4 } { b }$ 
B)  $\frac { 4 } { b ^ { \frac { 8 } { 7 } } }$ 
C)  $\frac { b } { 4 }$ 
D)  $\left( \frac { 4 } { b } \right) ^ { \frac { 8 } { 7 } }$

Question 9

Simplify. Express final results using positive exponents only. $\frac { 10 b ^ { \frac { 1 } { 4 } } } { 2 b ^ { \frac { 5 } { 4 } } }$

Accepted Answer

The answer of Simplify. Express final results using positive exponents...

Question 10

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { 3 } } { \sqrt { 11 } - \sqrt { 7 } }$

Accepted Answer

A)  $\frac { \sqrt { 33 } - \sqrt { 21 } } { 4 }$ 
B)  $\frac { \sqrt { 33 } + \sqrt { 21 } } { 18 }$ 
C)  $\frac { \sqrt { 33 } + \sqrt { 21 } } { 4 }$ 
D)  $\frac { \sqrt { 54 } } { 4 }$ 
A)  $\frac { \sqrt { 33 } - \sqrt { 21 } } { 4 }$ 
B)  $\frac { \sqrt { 33 } + \sqrt { 21 } } { 18 }$ 
C)  $\frac { \sqrt { 33 } + \sqrt { 21 } } { 4 }$ 
D)  $\frac { \sqrt { 54 } } { 4 }$

Question 11

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 12 x }$

Accepted Answer

A)  $2 \sqrt { 3 x }$ 
B)  $2 x \sqrt { 3 }$ 
C)  $4 \sqrt { 3 x }$ 
D)  $2 \sqrt { x }$ 
A)  $2 \sqrt { 3 x }$ 
B)  $2 x \sqrt { 3 }$ 
C)  $4 \sqrt { 3 x }$ 
D)  $2 \sqrt { x }$

Question 12

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 3 \sqrt { 49 x ^ { 3 } } - 8 \sqrt { 4 x ^ { 3 } } + 11 \sqrt { 81 x ^ { 3 } }$

Accepted Answer

A)  $0$ 
B)  $62 x \sqrt { x }$ 
C)  $62 \sqrt { x ^ { 3 } }$ 
D)  $712 x \sqrt { x }$ 
A)  $0$ 
B)  $62 x \sqrt { x }$ 
C)  $62 \sqrt { x ^ { 3 } }$ 
D)  $712 x \sqrt { x }$

Question 13

Write each of the following using positive rational exponents. Match each expression with the corresponding expression.
-$$\frac { 11 } { 13 }$$
$4 y$

Accepted Answer

A)  $4 \sqrt [ 13 ] { y ^ { 11 } }$ 
B)  $4 \sqrt [ 11 ] { y ^ { 13 } }$ 
A)  $4 \sqrt [ 13 ] { y ^ { 11 } }$ 
B)  $4 \sqrt [ 11 ] { y ^ { 13 } }$

Question 14

Simplify. Express final results using positive exponents only. $\left( 8 x ^ { \frac { 1 } { 7 } } \right) \left( 6 x ^ { \frac { 6 } { 7 } } \right)$

Accepted Answer

The answer of Simplify. Express final results using positive exponents...

Question 15

Using f = 0.35 as a coefficient of friction, determine how fast a car was traveling if it skidded D = 300 feet. Use the formula $S = \sqrt { 30 D f }$ Express your answer to the nearest mile per hour.

Accepted Answer

A)  63 miles per hour 
B)  51 miles per hour 
C)  43 miles per hour 
D)  56 miles per hour 
A)  63 miles per hour 
B)  51 miles per hour 
C)  43 miles per hour 
D)  56 miles per hour

Question 16

Change the radical to simplest radical form. $- \frac { 4 \sqrt { 20 } } { 6 \sqrt { 35 } }$

Accepted Answer

A)  $\frac { 35 \sqrt { 20 } } { 6 }$ 
B)  $- \frac { \sqrt { 35 } } { 21 }$ 
C)  $4 \sqrt { 7 }$ 
D)  $- \frac { 4 \sqrt { 7 } } { 21 }$ 
A)  $\frac { 35 \sqrt { 20 } } { 6 }$ 
B)  $- \frac { \sqrt { 35 } } { 21 }$ 
C)  $4 \sqrt { 7 }$ 
D)  $- \frac { 4 \sqrt { 7 } } { 21 }$

Question 17

The period of a pendulum is the time it takes to swing from one side to the other side and back. The formula $T = 2 \pi \sqrt { \frac { L } { 32 } }$ where T represents the time in seconds and L the length in feet, can be used to determine the period of a pendulum (see the figure). Find the period of a 4.5-feet pendulum. Express your answer to the nearest tenth of a second.

Accepted Answer

A)  2.7 seconds 
B)  3.1 seconds 
C)  2.6 seconds 
D)  2.4 seconds 
A)  2.7 seconds 
B)  3.1 seconds 
C)  2.6 seconds 
D)  2.4 seconds

Question 18

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $- 9 \sqrt { 7 } ( 3 \sqrt { 7 } + 2 \sqrt { 18 } )$

Accepted Answer

The answer of Find the following product and express answer...

Question 19

Solve the equation. $\sqrt { x ^ { 2 } + 5 } = 3$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(\sqrt { x ^...

Question 20

Solve the equation. $\sqrt { x ^ { 2 } - x + 9 } = x + 3$

Accepted Answer

A)  x = 3 
B)  x = 0 
C)  x = -3 
A)  x = 3 
B)  x = 0 
C)  x = -3

Simplify the expression. Express final results without using zero or negative integers as exponents. ( 3 x ⁴ y ^-5 ) ^-4

Solve the equation. $\sqrt { n + 9 } = n + 9$ Please enter your answer as two numbers, separated by a comma.

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { 5 } { \sqrt { b } + 4 }$ Please enter your answer as a fraction.

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement. - $54,880 \sqrt [ 3 ] { 3 }$

If b is a nonzero real number, then $b ^ { 0 } = 0$ .

Simplify the expression. Express final results without using zero or negative integers as exponents. a ⁴ a ^-7 a ^-2

Solve the equation. $\sqrt { 5 y - 29 } - 3 = 0$

Simplify. Express final results using positive exponents only. $\frac { 28 b ^ { \frac { 1 } { 7 } } } { 7 b ^ { \frac { 8 } { 7 } } }$

Simplify. Express final results using positive exponents only. $\frac { 10 b ^ { \frac { 1 } { 4 } } } { 2 b ^ { \frac { 5 } { 4 } } }$

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { 3 } } { \sqrt { 11 } - \sqrt { 7 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 12 x }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 3 \sqrt { 49 x ^ { 3 } } - 8 \sqrt { 4 x ^ { 3 } } + 11 \sqrt { 81 x ^ { 3 } }$

Write each of the following using positive rational exponents. Match each expression with the corresponding expression. - $\frac { 11 } { 13 }$ $4 y$

Simplify. Express final results using positive exponents only. $\left( 8 x ^ { \frac { 1 } { 7 } } \right) \left( 6 x ^ { \frac { 6 } { 7 } } \right)$

Using f = 0.35 as a coefficient of friction, determine how fast a car was traveling if it skidded D = 300 feet. Use the formula $S = \sqrt { 30 D f }$ Express your answer to the nearest mile per hour.

Change the radical to simplest radical form. $- \frac { 4 \sqrt { 20 } } { 6 \sqrt { 35 } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $- 9 \sqrt { 7 } ( 3 \sqrt { 7 } + 2 \sqrt { 18 } )$

Solve the equation. $\sqrt { x ^ { 2 } + 5 } = 3$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $\sqrt { x ^ { 2 } - x + 9 } = x + 3$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 10: Exponents and Radicals

Simplify the expression. Express final results without using zero or negative integers as exponents. ( 3 x 4 y -5 ) -4

Solve the equation. n+9=n+9\sqrt { n + 9 } = n + 9n+9​=n+9 Please enter your answer as two numbers, separated by a comma.

Rationalize the denominator and simplify. All variables represent positive real numbers. 5b+4\frac { 5 } { \sqrt { b } + 4 }b​+45​ Please enter your answer as a fraction.

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement. - 54,8803354,880 \sqrt [ 3 ] { 3 }54,88033​

If b is a nonzero real number, then b0=0b ^ { 0 } = 0b0=0 .

Simplify the expression. Express final results without using zero or negative integers as exponents. a 4 a -7 a -2

Solve the equation. 5y−29−3=0\sqrt { 5 y - 29 } - 3 = 05y−29​−3=0

Simplify. Express final results using positive exponents only. 28b177b87\frac { 28 b ^ { \frac { 1 } { 7 } } } { 7 b ^ { \frac { 8 } { 7 } } }7b78​28b71​​

Simplify. Express final results using positive exponents only. 10b142b54\frac { 10 b ^ { \frac { 1 } { 4 } } } { 2 b ^ { \frac { 5 } { 4 } } }2b45​10b41​​

Rationalize the denominator and simplify. All variables represent positive real numbers. 311−7\frac { \sqrt { 3 } } { \sqrt { 11 } - \sqrt { 7 } }11​−7​3​​

Express the following expression in simplest radical form. All variables represent positive real numbers. 12x\sqrt { 12 x }12x​

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. −349x3−84x3+1181x3- 3 \sqrt { 49 x ^ { 3 } } - 8 \sqrt { 4 x ^ { 3 } } + 11 \sqrt { 81 x ^ { 3 } }−349x3​−84x3​+1181x3​

Write each of the following using positive rational exponents. Match each expression with the corresponding expression. - 1113\frac { 11 } { 13 }1311​ 4y4 y4y

Simplify. Express final results using positive exponents only. (8x17)(6x67)\left( 8 x ^ { \frac { 1 } { 7 } } \right) \left( 6 x ^ { \frac { 6 } { 7 } } \right)(8x71​)(6x76​)

Using f = 0.35 as a coefficient of friction, determine how fast a car was traveling if it skidded D = 300 feet. Use the formula S=30DfS = \sqrt { 30 D f }S=30Df​ Express your answer to the nearest mile per hour.

Change the radical to simplest radical form. −420635- \frac { 4 \sqrt { 20 } } { 6 \sqrt { 35 } }−635​420​​

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. −97(37+218)- 9 \sqrt { 7 } ( 3 \sqrt { 7 } + 2 \sqrt { 18 } )−97​(37​+218​)

Solve the equation. x2+5=3\sqrt { x ^ { 2 } + 5 } = 3x2+5​=3 Please enter your answer as two numbers, separated by a comma.

Solve the equation. x2−x+9=x+3\sqrt { x ^ { 2 } - x + 9 } = x + 3x2−x+9​=x+3

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Simplify the expression. Express final results without using zero or negative integers as exponents. ( 3 x ⁴ y ^-5 ) ^-4

Solve the equation. $\sqrt { n + 9 } = n + 9$ Please enter your answer as two numbers, separated by a comma.

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { 5 } { \sqrt { b } + 4 }$ Please enter your answer as a fraction.

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement. - $54,880 \sqrt [ 3 ] { 3 }$

If b is a nonzero real number, then $b ^ { 0 } = 0$ .

Simplify the expression. Express final results without using zero or negative integers as exponents. a ⁴ a ^-7 a ^-2

Solve the equation. $\sqrt { 5 y - 29 } - 3 = 0$

Simplify. Express final results using positive exponents only. $\frac { 28 b ^ { \frac { 1 } { 7 } } } { 7 b ^ { \frac { 8 } { 7 } } }$

Simplify. Express final results using positive exponents only. $\frac { 10 b ^ { \frac { 1 } { 4 } } } { 2 b ^ { \frac { 5 } { 4 } } }$

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { 3 } } { \sqrt { 11 } - \sqrt { 7 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 12 x }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 3 \sqrt { 49 x ^ { 3 } } - 8 \sqrt { 4 x ^ { 3 } } + 11 \sqrt { 81 x ^ { 3 } }$

Write each of the following using positive rational exponents. Match each expression with the corresponding expression. - $\frac { 11 } { 13 }$ $4 y$

Simplify. Express final results using positive exponents only. $\left( 8 x ^ { \frac { 1 } { 7 } } \right) \left( 6 x ^ { \frac { 6 } { 7 } } \right)$

Using f = 0.35 as a coefficient of friction, determine how fast a car was traveling if it skidded D = 300 feet. Use the formula $S = \sqrt { 30 D f }$ Express your answer to the nearest mile per hour.

Change the radical to simplest radical form. $- \frac { 4 \sqrt { 20 } } { 6 \sqrt { 35 } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $- 9 \sqrt { 7 } ( 3 \sqrt { 7 } + 2 \sqrt { 18 } )$

Solve the equation. $\sqrt { x ^ { 2 } + 5 } = 3$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $\sqrt { x ^ { 2 } - x + 9 } = x + 3$