Question 1

Simplify the expression. Express final results without using zero or negative integers as exponents. ( a b 2 c - 1 ) - 5

Accepted Answer

A)  $\frac { c ^ { 5 } } { a ^ { 5 } b ^ { 10 } }$ 
B)  $\frac { a ^ { 5 } b ^ { 10 } } { c ^ { 5 } }$ 
C)  $a ^ { 5 } b ^ { 10 } c ^ { 5 }$ 
A)  $\frac { c ^ { 5 } } { a ^ { 5 } b ^ { 10 } }$ 
B)  $\frac { a ^ { 5 } b ^ { 10 } } { c ^ { 5 } }$ 
C)  $a ^ { 5 } b ^ { 10 } c ^ { 5 }$

Question 2

In order to be multiplied, radicals must have the same index and the same radicand.

Accepted Answer

A) True 
 B)False

Question 3

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { 6 } } { 3 \sqrt { 2 } + 2 \sqrt { 3 } }$

Accepted Answer

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

Question 4

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $8 \sqrt { 45 x ^ { 5 } } - 2 \sqrt { 80 x ^ { 5 } } + 4 \sqrt { 125 x ^ { 5 } }$

Accepted Answer

A)  $36 x ^ { 3 }$ 
B)  $36 x ^ { 2 } \sqrt { 5 x }$ 
C)  $36 x \sqrt { 5 x }$ 
D)  $36 x ^ { 2 } \sqrt { 5 }$ 
A)  $36 x ^ { 3 }$ 
B)  $36 x ^ { 2 } \sqrt { 5 x }$ 
C)  $36 x \sqrt { 5 x }$ 
D)  $36 x ^ { 2 } \sqrt { 5 }$

Question 5

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 5 } { 18 x ^ { 2 } } }$

Accepted Answer

The answer of Express the following expression in simplest radical...

Question 6

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt [ 3 ] { 75 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }$

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 25 x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }$ 
B)  $\frac { 5 \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }$ 
C)  $\frac { \sqrt [ 3 ] { 25 x y } } { y }$ 
D)  $\frac { 25 \sqrt [ 3 ] { x y } } { x y ^ { 2 } }$ 
A)  $\frac { \sqrt [ 3 ] { 25 x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }$ 
B)  $\frac { 5 \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }$ 
C)  $\frac { \sqrt [ 3 ] { 25 x y } } { y }$ 
D)  $\frac { 25 \sqrt [ 3 ] { x y } } { x y ^ { 2 } }$

Question 7

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 8 \sqrt { 17 } - 9 \sqrt { 119 } ) ( 7 \sqrt { 343 } + \sqrt { 119 } )$

Accepted Answer

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

Question 8

Simplify the numerical expression. 3S1U1P19 S1S1P03S1U1P1-4S1S1P0

Accepted Answer

A)  1,594,323 
B)  243 
C)  729 
A)  1,594,323 
B)  243 
C)  729

Question 9

Solve the equation. $\sqrt { 6 x } = 24$

Accepted Answer

A)  x = 96 
B)  x = 6 
C)  x = 24 
A)  x = 96 
B)  x = 6 
C)  x = 24

Question 10

Evaluate. $\sqrt [ 3 ] { 64 }$

Accepted Answer

A)  4 
B)  16 
C)  1 
D)  8 
A)  4 
B)  16 
C)  1 
D)  8

Question 11

Evaluate the numerical expression. $- 16 ^ { \frac { 1 } { 2 } }$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $-$ 8 
C)  $-$ 4 
D)  No correct answer defined. 
A)  $\frac { 1 } { 4 }$ 
B)  $-$ 8 
C)  $-$ 4 
D)  No correct answer defined.

Question 12

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $- 5 \sqrt { 3 } ( 6 \sqrt { 3 } + 4 \sqrt { 20 } )$

Accepted Answer

A)  $- 30 \sqrt { 3 } - 20 \sqrt { 20 }$ 
B)  $- 90 - 40 \sqrt { 2 }$ 
C)  $- 40 - 90 \sqrt { 3 }$ 
D)  $- 90 - 40 \sqrt { 15 }$ 
A)  $- 30 \sqrt { 3 } - 20 \sqrt { 20 }$ 
B)  $- 90 - 40 \sqrt { 2 }$ 
C)  $- 40 - 90 \sqrt { 3 }$ 
D)  $- 90 - 40 \sqrt { 15 }$

Question 13

Simplify the numerical expression. $- \left( \frac { 1 } { 4 } \right) ^ { - 4 }$

Accepted Answer

The answer of Simplify the numerical expression. \(- \left( \frac...

Question 14

Change the radical to simplest radical form. $\sqrt { 20 }$

Accepted Answer

The answer of Change the radical to simplest radical form....

Question 15

Use the distributive property to help simplify the expression. $- \frac { 2 } { 3 } \sqrt { 18 } + \frac { 4 } { 5 } \sqrt { 32 } - \frac { 5 } { 6 } \sqrt { 50 }$

Accepted Answer

The answer of Use the distributive property to help simplify...

Question 16

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 54 y }$

Accepted Answer

A)  $3 \sqrt [ 3 ] { 2 y }$ 
B)  $\sqrt [ 3 ] { 2 y }$ 
C)  $3 \sqrt [ 3 ] { y }$ 
D)  $3 y ^ { 3 } \sqrt [ 3 ] { 2 }$ 
A)  $3 \sqrt [ 3 ] { 2 y }$ 
B)  $\sqrt [ 3 ] { 2 y }$ 
C)  $3 \sqrt [ 3 ] { y }$ 
D)  $3 y ^ { 3 } \sqrt [ 3 ] { 2 }$

Question 17

Simplify the numerical expression. ( 3 2 2 -1 ) 2 Please enter your answer as a fraction.

Accepted Answer

Question 18

Write $9 \sqrt [ 3 ] { m }$ using positive rational exponents.

Accepted Answer

The answer of Write \(9 \sqrt [ 3 ] {...

Question 19

Perform. $\frac { \sqrt [ 3 ] { 9 } } { \sqrt [ 4 ] { 9 } }$ Express answers in simplest radical form.

Accepted Answer

A)  $\frac { 1 } { \sqrt [ 12 ] { 9 } }$ 
B)  $\sqrt [ 12 ] { 81 }$ 
C)  $\sqrt [ 7 ] { 9 }$ 
D)  $\sqrt [ 12 ] { 9 }$ 
A)  $\frac { 1 } { \sqrt [ 12 ] { 9 } }$ 
B)  $\sqrt [ 12 ] { 81 }$ 
C)  $\sqrt [ 7 ] { 9 }$ 
D)  $\sqrt [ 12 ] { 9 }$

Question 20

Change the radical to simplest radical form. $\sqrt { \frac { 2 } { 11 } }$

Accepted Answer

The answer of Change the radical to simplest radical form....

Simplify the expression. Express final results without using zero or negative integers as exponents. ( a b ² c ^{- 1} ) ^{- 5}

In order to be multiplied, radicals must have the same index and the same radicand.

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { 6 } } { 3 \sqrt { 2 } + 2 \sqrt { 3 } }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $8 \sqrt { 45 x ^ { 5 } } - 2 \sqrt { 80 x ^ { 5 } } + 4 \sqrt { 125 x ^ { 5 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 5 } { 18 x ^ { 2 } } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt [ 3 ] { 75 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 8 \sqrt { 17 } - 9 \sqrt { 119 } ) ( 7 \sqrt { 343 } + \sqrt { 119 } )$

Simplify the numerical expression. 3⁹3^-4

Solve the equation. $\sqrt { 6 x } = 24$

Evaluate. $\sqrt [ 3 ] { 64 }$

Evaluate the numerical expression. $- 16 ^ { \frac { 1 } { 2 } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $- 5 \sqrt { 3 } ( 6 \sqrt { 3 } + 4 \sqrt { 20 } )$

Simplify the numerical expression. $- \left( \frac { 1 } { 4 } \right) ^ { - 4 }$

Change the radical to simplest radical form. $\sqrt { 20 }$

Use the distributive property to help simplify the expression. $- \frac { 2 } { 3 } \sqrt { 18 } + \frac { 4 } { 5 } \sqrt { 32 } - \frac { 5 } { 6 } \sqrt { 50 }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 54 y }$

Simplify the numerical expression. ( 3²2^-1) ² Please enter your answer as a fraction.

Write $9 \sqrt [ 3 ] { m }$ using positive rational exponents.

Perform. $\frac { \sqrt [ 3 ] { 9 } } { \sqrt [ 4 ] { 9 } }$ Express answers in simplest radical form.

Change the radical to simplest radical form. $\sqrt { \frac { 2 } { 11 } }$

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. ( a b 2 c - 1 ) - 5

In order to be multiplied, radicals must have the same index and the same radicand.

Rationalize the denominator and simplify. All variables represent positive real numbers. 632+23\frac { \sqrt { 6 } } { 3 \sqrt { 2 } + 2 \sqrt { 3 } }32​+23​6​​

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. 845x5−280x5+4125x58 \sqrt { 45 x ^ { 5 } } - 2 \sqrt { 80 x ^ { 5 } } + 4 \sqrt { 125 x ^ { 5 } }845x5​−280x5​+4125x5​

Express the following expression in simplest radical form. All variables represent positive real numbers. 518x2\sqrt { \frac { 5 } { 18 x ^ { 2 } } }18x25​​

Express the following expression in simplest radical form. All variables represent positive real numbers. 75xy33x2y53\frac { \sqrt [ 3 ] { 75 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }33x2y5​375xy​​

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. (817−9119)(7343+119)( 8 \sqrt { 17 } - 9 \sqrt { 119 } ) ( 7 \sqrt { 343 } + \sqrt { 119 } )(817​−9119​)(7343​+119​)

Simplify the numerical expression. 39 3-4

Solve the equation. 6x=24\sqrt { 6 x } = 246x​=24

Evaluate. 643\sqrt [ 3 ] { 64 }364​

Evaluate the numerical expression. −1612- 16 ^ { \frac { 1 } { 2 } }−1621​

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. −53(63+420)- 5 \sqrt { 3 } ( 6 \sqrt { 3 } + 4 \sqrt { 20 } )−53​(63​+420​)

Simplify the numerical expression. −(14)−4- \left( \frac { 1 } { 4 } \right) ^ { - 4 }−(41​)−4

Change the radical to simplest radical form. 20\sqrt { 20 }20​

Use the distributive property to help simplify the expression. −2318+4532−5650- \frac { 2 } { 3 } \sqrt { 18 } + \frac { 4 } { 5 } \sqrt { 32 } - \frac { 5 } { 6 } \sqrt { 50 }−32​18​+54​32​−65​50​

Express the following expression in simplest radical form. All variables represent positive real numbers. 54y3\sqrt [ 3 ] { 54 y }354y​

Simplify the numerical expression. ( 3 2 2 -1 ) 2 Please enter your answer as a fraction.

Write 9m39 \sqrt [ 3 ] { m }93m​ using positive rational exponents.

Perform. 9394\frac { \sqrt [ 3 ] { 9 } } { \sqrt [ 4 ] { 9 } }49​39​​ Express answers in simplest radical form.

Change the radical to simplest radical form. 211\sqrt { \frac { 2 } { 11 } }112​​

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. ( a b ² c ^{- 1} ) ^{- 5}

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { 6 } } { 3 \sqrt { 2 } + 2 \sqrt { 3 } }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $8 \sqrt { 45 x ^ { 5 } } - 2 \sqrt { 80 x ^ { 5 } } + 4 \sqrt { 125 x ^ { 5 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 5 } { 18 x ^ { 2 } } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt [ 3 ] { 75 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 8 \sqrt { 17 } - 9 \sqrt { 119 } ) ( 7 \sqrt { 343 } + \sqrt { 119 } )$

Simplify the numerical expression. 3⁹3^-4

Solve the equation. $\sqrt { 6 x } = 24$

Evaluate. $\sqrt [ 3 ] { 64 }$

Evaluate the numerical expression. $- 16 ^ { \frac { 1 } { 2 } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $- 5 \sqrt { 3 } ( 6 \sqrt { 3 } + 4 \sqrt { 20 } )$

Simplify the numerical expression. $- \left( \frac { 1 } { 4 } \right) ^ { - 4 }$

Change the radical to simplest radical form. $\sqrt { 20 }$

Use the distributive property to help simplify the expression. $- \frac { 2 } { 3 } \sqrt { 18 } + \frac { 4 } { 5 } \sqrt { 32 } - \frac { 5 } { 6 } \sqrt { 50 }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 54 y }$

Simplify the numerical expression. ( 3²2^-1) ² Please enter your answer as a fraction.

Write $9 \sqrt [ 3 ] { m }$ using positive rational exponents.

Perform. $\frac { \sqrt [ 3 ] { 9 } } { \sqrt [ 4 ] { 9 } }$ Express answers in simplest radical form.

Change the radical to simplest radical form. $\sqrt { \frac { 2 } { 11 } }$