Question 1

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 10 } } { \sqrt [ 3 ] { 2 } }$

Accepted Answer

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

Question 2

Use the distributive property to help simplify the expression. $\frac { 4 } { 5 } \sqrt { 3 } - \frac { 3 } { 4 } \sqrt { 12 }$

Accepted Answer

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

Question 3

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement.
-$98 \sqrt { 2 }$

Accepted Answer

A)  $( 7 \sqrt { 7 } ) ( 2 \sqrt { 14 } )$ 
B)  $( 4 \sqrt { 3 } ) ( - 14 \sqrt { 2 } )$ 
C)  $( - 3 \sqrt { 3 } ) ( - 4 \sqrt { 8 } )$ 
D)  $( 2 \sqrt { 14 } ) ( 4 \sqrt { 14 } )$ 
A)  $( 7 \sqrt { 7 } ) ( 2 \sqrt { 14 } )$ 
B)  $( 4 \sqrt { 3 } ) ( - 14 \sqrt { 2 } )$ 
C)  $( - 3 \sqrt { 3 } ) ( - 4 \sqrt { 8 } )$ 
D)  $( 2 \sqrt { 14 } ) ( 4 \sqrt { 14 } )$

Question 4

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement.
-$64 \sqrt { 11 a } + 8 \sqrt { a d }$

Accepted Answer

A)  $8 \sqrt { a } ( 8 \sqrt { 11 } + \sqrt { d } )$ 
B)  $\sqrt { 11 a } ( 64 \sqrt { d } - 8 \sqrt { 7 } )$ 
C)  $8 \sqrt { a } ( 8 \sqrt { a d } + 8 \sqrt { a } )$ 
D)  $\sqrt { 7 d } \left( \sqrt { 1,331 a d } + \sqrt { 605 d ^ { 2 } } \right)$ 
A)  $8 \sqrt { a } ( 8 \sqrt { 11 } + \sqrt { d } )$ 
B)  $\sqrt { 11 a } ( 64 \sqrt { d } - 8 \sqrt { 7 } )$ 
C)  $8 \sqrt { a } ( 8 \sqrt { a d } + 8 \sqrt { a } )$ 
D)  $\sqrt { 7 d } \left( \sqrt { 1,331 a d } + \sqrt { 605 d ^ { 2 } } \right)$

Question 5

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $4 \sqrt { 27 x ^ { 5 } } - 7 \sqrt { 48 x ^ { 5 } } + 8 \sqrt { 75 x ^ { 5 } }$

Accepted Answer

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

Question 6

Solve the equation. $\sqrt { 4 x - 4 } - \sqrt { 3 x + 1 } = 0$

Accepted Answer

The answer of Solve the equation. \(\sqrt { 4 x...

Question 7

Change the radical to simplest radical form. $\sqrt [ 3 ] { 54 }$

Accepted Answer

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

Question 8

Write $- \sqrt [ 6 ] { x + y }$ using positive rational exponents.

Accepted Answer

A)  $( x + y ) ^ { - \frac { 1 } { 6 } }$ 
B)  $( - x - y ) ^ { \frac { 1 } { 6 } }$ 
C)  $- ( x + y ) ^ { \frac { 1 } { 6 } }$ 
D)  $- ( x + y ) ^ { 6 }$ 
A)  $( x + y ) ^ { - \frac { 1 } { 6 } }$ 
B)  $( - x - y ) ^ { \frac { 1 } { 6 } }$ 
C)  $- ( x + y ) ^ { \frac { 1 } { 6 } }$ 
D)  $- ( x + y ) ^ { 6 }$

Question 9

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 y }$

Accepted Answer

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

Question 10

Multiply and simplify where possible. $\sqrt { 8 } \sqrt { 14 }$

Accepted Answer

The answer of Multiply and simplify where possible. \(\sqrt {...

Question 11

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

Accepted Answer

The answer of Evaluate the numerical expression. \(16 ^ {...

Question 12

A radical with a fraction in lowest terms within the radical sign is simplified.

Accepted Answer

A) True 
 B)False

Question 13

Evaluate the numerical expression. $\left( \frac { 1 } { 36 } \right) ^ { - \frac { 3 } { 2 } }$

Accepted Answer

A)  6 
B)  36 
C)  $\frac { 1 } { 216 }$ 
D)  216 
A)  6 
B)  36 
C)  $\frac { 1 } { 216 }$ 
D)  216

Question 14

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

Accepted Answer

A)  $42 x ^ { \frac { 1 } { 8 } }$ 
B)  $7 x$ 
C)  $42 x$ 
D)  $42 x ^ { 2 }$ 
A)  $42 x ^ { \frac { 1 } { 8 } }$ 
B)  $7 x$ 
C)  $42 x$ 
D)  $42 x ^ { 2 }$

Question 15

Change the radical to simplest radical form. $- 7 \sqrt [ 3 ] { 54 }$

Accepted Answer

A)  $14 \sqrt [ 3 ] { 3 }$ 
B)  $- 21 \sqrt [ 3 ] { 2 }$ 
C)  21 
D)  $- 7 \sqrt [ 3 ] { 2 }$ 
A)  $14 \sqrt [ 3 ] { 3 }$ 
B)  $- 21 \sqrt [ 3 ] { 2 }$ 
C)  21 
D)  $- 7 \sqrt [ 3 ] { 2 }$

Question 16

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

Accepted Answer

A)  $- \frac { 14 \sqrt { 2 } } { 15 }$ 
B)  $\frac { 26 \sqrt { 2 } } { 25 }$ 
C)  $- \frac { \sqrt { 2 } } { 21 }$ 
D)  $- \frac { 21 \sqrt { 2 } } { 10 }$ 
A)  $- \frac { 14 \sqrt { 2 } } { 15 }$ 
B)  $\frac { 26 \sqrt { 2 } } { 25 }$ 
C)  $- \frac { \sqrt { 2 } } { 21 }$ 
D)  $- \frac { 21 \sqrt { 2 } } { 10 }$

Question 17

Write $5 \sqrt [ 4 ] { y ^ { 5 } }$ using positive rational exponents.

Accepted Answer

A)  $( 5 y ) ^ { \frac { 5 } { 4 } }$ 
B)  $\frac { 4 } { 5 }$ 
C)  $5 y ^ { \frac { 5 } { 4 } }$ 
D)  $y ^ { \frac { 5 } { 4 } }$ 
A)  $( 5 y ) ^ { \frac { 5 } { 4 } }$ 
B)  $\frac { 4 } { 5 }$ 
C)  $5 y ^ { \frac { 5 } { 4 } }$ 
D)  $y ^ { \frac { 5 } { 4 } }$

Question 18

Find the indicated product. Express final results using positive integral exponents only. (4 xy - 4)(9 x - 4 y 8) Please enter your answer as a fraction.

Accepted Answer

Question 19

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 3 \sqrt { 11 } - 4 \sqrt { 7 } ) ( 14 \sqrt { 11 } - 18 \sqrt { 7 } )$

Accepted Answer

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

Question 20

Evaluate the numerical expression. $( - 216 ) ^ { \frac { 1 } { 3 } }$

Accepted Answer

To evaluate the numerical expression (-2

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 10 } } { \sqrt [ 3 ] { 2 } }$

Use the distributive property to help simplify the expression. $\frac { 4 } { 5 } \sqrt { 3 } - \frac { 3 } { 4 } \sqrt { 12 }$

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - $98 \sqrt { 2 }$

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $64 \sqrt { 11 a } + 8 \sqrt { a d }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $4 \sqrt { 27 x ^ { 5 } } - 7 \sqrt { 48 x ^ { 5 } } + 8 \sqrt { 75 x ^ { 5 } }$

Solve the equation. $\sqrt { 4 x - 4 } - \sqrt { 3 x + 1 } = 0$

Change the radical to simplest radical form. $\sqrt [ 3 ] { 54 }$

Write $- \sqrt [ 6 ] { x + y }$ using positive rational exponents.

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 y }$

Multiply and simplify where possible. $\sqrt { 8 } \sqrt { 14 }$

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

A radical with a fraction in lowest terms within the radical sign is simplified.

Evaluate the numerical expression. $\left( \frac { 1 } { 36 } \right) ^ { - \frac { 3 } { 2 } }$

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

Change the radical to simplest radical form. $- 7 \sqrt [ 3 ] { 54 }$

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

Write $5 \sqrt [ 4 ] { y ^ { 5 } }$ using positive rational exponents.

Find the indicated product. Express final results using positive integral exponents only. (4 xy ^{- 4})(9 x ^{- 4} y ⁸) Please enter your answer as a fraction.

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 3 \sqrt { 11 } - 4 \sqrt { 7 } ) ( 14 \sqrt { 11 } - 18 \sqrt { 7 } )$

Evaluate the numerical expression. $( - 216 ) ^ { \frac { 1 } { 3 } }$

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

Change the radical to simplest radical form. 10323\frac { \sqrt [ 3 ] { 10 } } { \sqrt [ 3 ] { 2 } }32​310​​

Use the distributive property to help simplify the expression. 453−3412\frac { 4 } { 5 } \sqrt { 3 } - \frac { 3 } { 4 } \sqrt { 12 }54​3​−43​12​

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - 98298 \sqrt { 2 }982​

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - 6411a+8ad64 \sqrt { 11 a } + 8 \sqrt { a d }6411a​+8ad​

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. 427x5−748x5+875x54 \sqrt { 27 x ^ { 5 } } - 7 \sqrt { 48 x ^ { 5 } } + 8 \sqrt { 75 x ^ { 5 } }427x5​−748x5​+875x5​

Solve the equation. 4x−4−3x+1=0\sqrt { 4 x - 4 } - \sqrt { 3 x + 1 } = 04x−4​−3x+1​=0

Change the radical to simplest radical form. 543\sqrt [ 3 ] { 54 }354​

Write −x+y6- \sqrt [ 6 ] { x + y }−6x+y​ using positive rational exponents.

Express the following expression in simplest radical form. All variables represent positive real numbers. 16y3\sqrt [ 3 ] { 16 y }316y​

Multiply and simplify where possible. 814\sqrt { 8 } \sqrt { 14 }8​14​

Evaluate the numerical expression. 161216 ^ { \frac { 1 } { 2 } }1621​

A radical with a fraction in lowest terms within the radical sign is simplified.

Evaluate the numerical expression. (136)−32\left( \frac { 1 } { 36 } \right) ^ { - \frac { 3 } { 2 } }(361​)−23​

Simplify. Express final results using positive exponents only. (7x18)(6x78)\left( 7 x ^ { \frac { 1 } { 8 } } \right) \left( 6 x ^ { \frac { 7 } { 8 } } \right)(7x81​)(6x87​)

Change the radical to simplest radical form. −7543- 7 \sqrt [ 3 ] { 54 }−7354​

Use the distributive property to help simplify the expression. −2318+4518−5618- \frac { 2 } { 3 } \sqrt { 18 } + \frac { 4 } { 5 } \sqrt { 18 } - \frac { 5 } { 6 } \sqrt { 18 }−32​18​+54​18​−65​18​

Write 5y545 \sqrt [ 4 ] { y ^ { 5 } }54y5​ using positive rational exponents.

Find the indicated product. Express final results using positive integral exponents only. (4 xy - 4)(9 x - 4 y 8) Please enter your answer as a fraction.

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. (311−47)(1411−187)( 3 \sqrt { 11 } - 4 \sqrt { 7 } ) ( 14 \sqrt { 11 } - 18 \sqrt { 7 } )(311​−47​)(1411​−187​)

Evaluate the numerical expression. (−216)13( - 216 ) ^ { \frac { 1 } { 3 } }(−216)31​

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

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 10 } } { \sqrt [ 3 ] { 2 } }$

Use the distributive property to help simplify the expression. $\frac { 4 } { 5 } \sqrt { 3 } - \frac { 3 } { 4 } \sqrt { 12 }$

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - $98 \sqrt { 2 }$

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $64 \sqrt { 11 a } + 8 \sqrt { a d }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $4 \sqrt { 27 x ^ { 5 } } - 7 \sqrt { 48 x ^ { 5 } } + 8 \sqrt { 75 x ^ { 5 } }$

Solve the equation. $\sqrt { 4 x - 4 } - \sqrt { 3 x + 1 } = 0$

Change the radical to simplest radical form. $\sqrt [ 3 ] { 54 }$

Write $- \sqrt [ 6 ] { x + y }$ using positive rational exponents.

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 y }$

Multiply and simplify where possible. $\sqrt { 8 } \sqrt { 14 }$

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

Evaluate the numerical expression. $\left( \frac { 1 } { 36 } \right) ^ { - \frac { 3 } { 2 } }$

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

Change the radical to simplest radical form. $- 7 \sqrt [ 3 ] { 54 }$

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

Write $5 \sqrt [ 4 ] { y ^ { 5 } }$ using positive rational exponents.

Find the indicated product. Express final results using positive integral exponents only. (4 xy ^{- 4})(9 x ^{- 4} y ⁸) Please enter your answer as a fraction.

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 3 \sqrt { 11 } - 4 \sqrt { 7 } ) ( 14 \sqrt { 11 } - 18 \sqrt { 7 } )$

Evaluate the numerical expression. $( - 216 ) ^ { \frac { 1 } { 3 } }$