Question 1

Evaluate the numerical expression. $- 9 ^ { \frac { 1 } { 2 } }$

Accepted Answer

The expression - 9 ^ { \frac { 1 } { 2 }

Question 2

Find, to the nearest square yard, the area of a triangular plot of ground that measures 5 yards by 8 yards by 6 yards.

Accepted Answer

The answer of Find, to the nearest square yard, the...

Question 3

Solve the equation. $\sqrt [ 3 ] { x - 5 } = 3$

Accepted Answer

A)  x = 32, x = 1 
B)  x = 32 
C)  x = 32, x = -32 
A)  x = 32, x = 1 
B)  x = 32 
C)  x = 32, x = -32

Question 4

Evaluate. $\sqrt { 9 }$

Accepted Answer

The answer of Evaluate. $\sqrt { 9 }$...

Question 5

Express the following as a single fraction involving positive exponents only. 2 x - 3 - 3 x - 5 Please enter your answer as a fraction.

Accepted Answer

Question 6

When using the property If $a = b$ , then $a ^ { n } = b ^ { n }$ , all potential solutions must be checked in the original equation.

Accepted Answer

A) True 
 B)False

Question 7

Solve each equation. Match each equation with the corresponding solution.
-$n = \frac { 121 } { 36 }$

Accepted Answer

A)  $6 \sqrt { n } = 11$ 
B)  $11 \sqrt { n } = 6$ 
A)  $6 \sqrt { n } = 11$ 
B)  $11 \sqrt { n } = 6$

Question 8

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement.
-$3,920$

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 9

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement.
-$24 \sqrt { 6 }$

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 10

Use the distributive property to help simplify the expression. $2 \sqrt [ 3 ] { 3 } + 2 \sqrt [ 3 ] { 81 } - 2 \sqrt [ 3 ] { 24 }$

Accepted Answer

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

Question 11

Solve the equation. $\sqrt { n - 18 } + \sqrt { n + 18 } = 2 \sqrt { n - 3 }$

Accepted Answer

A)  n = $-$ 30 
B)  n = 3 
C)  n = 30 
A)  n = $-$ 30 
B)  n = 3 
C)  n = 30

Question 12

Solve the equation. $3 \sqrt { m - 2 } = 7$

Accepted Answer

A)  $m = \frac { 31 } { 9 }$ 
B)  $m = \frac { 67 } { 9 }$ 
C)  $m = \frac { 13 } { 3 }$ 
D)  $m = \frac { 51 } { 9 }$ 
A)  $m = \frac { 31 } { 9 }$ 
B)  $m = \frac { 67 } { 9 }$ 
C)  $m = \frac { 13 } { 3 }$ 
D)  $m = \frac { 51 } { 9 }$

Question 13

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 128 y ^ { 3 } } { 49 x } }$

Accepted Answer

A)  $\frac { 8 y \sqrt { 2 x y } } { 7 }$ 
B)  $\frac { 8 y ^ { 2 } \sqrt { 2 x y } } { x }$ 
C)  $\frac { 8 y \sqrt { 2 x y } } { 7 x }$ 
D)  $\frac { 8 \sqrt { 2 x y } } { 7 x }$ 
A)  $\frac { 8 y \sqrt { 2 x y } } { 7 }$ 
B)  $\frac { 8 y ^ { 2 } \sqrt { 2 x y } } { x }$ 
C)  $\frac { 8 y \sqrt { 2 x y } } { 7 x }$ 
D)  $\frac { 8 \sqrt { 2 x y } } { 7 x }$

Question 14

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 3 \sqrt { 4 x } + 3 \sqrt { 9 x } + 5 \sqrt { 16 x }$

Accepted Answer

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

Question 15

Simplify the numerical expression. ( 4 -1 ) - 2

Accepted Answer

Question 16

Solve the equation. $\sqrt { 7 x - 2 } - \sqrt { 2 x + 23 } = 0$

Accepted Answer

A)  x = 23 
B)  x = 2 
C)  x = 5 
A)  x = 23 
B)  x = 2 
C)  x = 5

Question 17

Solve the equation. $\sqrt [ 3 ] { 5 x - 3 } = \sqrt [ 3 ] { 2 - 4 x }$

Accepted Answer

A)  $x = \frac { 9 } { 5 }$ 
B)  $x = \frac { 5 } { 9 }$ 
C)  $x = \frac { 1 } { 9 }$ 
A)  $x = \frac { 9 } { 5 }$ 
B)  $x = \frac { 5 } { 9 }$ 
C)  $x = \frac { 1 } { 9 }$

Question 18

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { 13 } ( \sqrt { 7 } + \sqrt { 3 } )$

Accepted Answer

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

Question 19

Simplify. Express final results using positive exponents only. $\left( 5 y x ^ { \frac { 1 } { 4 } } \right) ^ { 4 }$

Accepted Answer

A)  $625 x y ^ { 4 }$ 
B)  $625 x y ^ { \frac { 1 } { 4 } }$ 
C)  $625 y x ^ { 4 }$ 
D)  $5 x y ^ { 4 }$ 
A)  $625 x y ^ { 4 }$ 
B)  $625 x y ^ { \frac { 1 } { 4 } }$ 
C)  $625 y x ^ { 4 }$ 
D)  $5 x y ^ { 4 }$

Question 20

Find the indicated quotients. Express final results using positive integral exponents only. $\left( \frac { 28 x ^ { - 2 } y ^ { - 3 } } { 4 x ^ { 7 } y ^ { 8 } } \right) ^ { - 1 }$

Accepted Answer

A)  $\frac { 7 } { x ^ { 9 } y ^ { 11 } }$ 
B)  $7 x ^ { 9 } y ^ { 11 }$ 
C)  $\frac { x ^ { 9 } y ^ { 11 } } { 7 }$ 
A)  $\frac { 7 } { x ^ { 9 } y ^ { 11 } }$ 
B)  $7 x ^ { 9 } y ^ { 11 }$ 
C)  $\frac { x ^ { 9 } y ^ { 11 } } { 7 }$

Evaluate the numerical expression. $- 9 ^ { \frac { 1 } { 2 } }$

Find, to the nearest square yard, the area of a triangular plot of ground that measures 5 yards by 8 yards by 6 yards.

Solve the equation. $\sqrt [ 3 ] { x - 5 } = 3$

Evaluate. $\sqrt { 9 }$

Express the following as a single fraction involving positive exponents only. 2 x ^{- 3} - 3 x ^{- 5} Please enter your answer as a fraction.

When using the property If $a = b$ , then $a ^ { n } = b ^ { n }$ , all potential solutions must be checked in the original equation.

Solve each equation. Match each equation with the corresponding solution. - $n = \frac { 121 } { 36 }$

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement. - $3,920$

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - $24 \sqrt { 6 }$

Use the distributive property to help simplify the expression. $2 \sqrt [ 3 ] { 3 } + 2 \sqrt [ 3 ] { 81 } - 2 \sqrt [ 3 ] { 24 }$

Solve the equation. $\sqrt { n - 18 } + \sqrt { n + 18 } = 2 \sqrt { n - 3 }$

Solve the equation. $3 \sqrt { m - 2 } = 7$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 128 y ^ { 3 } } { 49 x } }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 3 \sqrt { 4 x } + 3 \sqrt { 9 x } + 5 \sqrt { 16 x }$

Simplify the numerical expression. ( 4^-1) ^{- 2}

Solve the equation. $\sqrt { 7 x - 2 } - \sqrt { 2 x + 23 } = 0$

Solve the equation. $\sqrt [ 3 ] { 5 x - 3 } = \sqrt [ 3 ] { 2 - 4 x }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { 13 } ( \sqrt { 7 } + \sqrt { 3 } )$

Simplify. Express final results using positive exponents only. $\left( 5 y x ^ { \frac { 1 } { 4 } } \right) ^ { 4 }$

Find the indicated quotients. Express final results using positive integral exponents only. $\left( \frac { 28 x ^ { - 2 } y ^ { - 3 } } { 4 x ^ { 7 } y ^ { 8 } } \right) ^ { - 1 }$

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

Evaluate the numerical expression. −912- 9 ^ { \frac { 1 } { 2 } }−921​

Find, to the nearest square yard, the area of a triangular plot of ground that measures 5 yards by 8 yards by 6 yards.

Solve the equation. x−53=3\sqrt [ 3 ] { x - 5 } = 33x−5​=3

Evaluate. 9\sqrt { 9 }9​

Express the following as a single fraction involving positive exponents only. 2 x - 3 - 3 x - 5 Please enter your answer as a fraction.

When using the property If a=ba = ba=b , then an=bna ^ { n } = b ^ { n }an=bn , all potential solutions must be checked in the original equation.

Solve each equation. Match each equation with the corresponding solution. - n=12136n = \frac { 121 } { 36 }n=36121​

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement. - 3,9203,9203,920

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - 24624 \sqrt { 6 }246​

Use the distributive property to help simplify the expression. 233+2813−22432 \sqrt [ 3 ] { 3 } + 2 \sqrt [ 3 ] { 81 } - 2 \sqrt [ 3 ] { 24 }233​+2381​−2324​

Solve the equation. n−18+n+18=2n−3\sqrt { n - 18 } + \sqrt { n + 18 } = 2 \sqrt { n - 3 }n−18​+n+18​=2n−3​

Solve the equation. 3m−2=73 \sqrt { m - 2 } = 73m−2​=7

Express the following expression in simplest radical form. All variables represent positive real numbers. 128y349x\sqrt { \frac { 128 y ^ { 3 } } { 49 x } }49x128y3​​

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. −34x+39x+516x- 3 \sqrt { 4 x } + 3 \sqrt { 9 x } + 5 \sqrt { 16 x }−34x​+39x​+516x​

Simplify the numerical expression. ( 4 -1 ) - 2

Solve the equation. 7x−2−2x+23=0\sqrt { 7 x - 2 } - \sqrt { 2 x + 23 } = 07x−2​−2x+23​=0

Solve the equation. 5x−33=2−4x3\sqrt [ 3 ] { 5 x - 3 } = \sqrt [ 3 ] { 2 - 4 x }35x−3​=32−4x​

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. 13(7+3)\sqrt { 13 } ( \sqrt { 7 } + \sqrt { 3 } )13​(7​+3​)

Simplify. Express final results using positive exponents only. (5yx14)4\left( 5 y x ^ { \frac { 1 } { 4 } } \right) ^ { 4 }(5yx41​)4

Find the indicated quotients. Express final results using positive integral exponents only. (28x−2y−34x7y8)−1\left( \frac { 28 x ^ { - 2 } y ^ { - 3 } } { 4 x ^ { 7 } y ^ { 8 } } \right) ^ { - 1 }(4x7y828x−2y−3​)−1

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

Evaluate the numerical expression. $- 9 ^ { \frac { 1 } { 2 } }$

Solve the equation. $\sqrt [ 3 ] { x - 5 } = 3$

Evaluate. $\sqrt { 9 }$

Express the following as a single fraction involving positive exponents only. 2 x ^{- 3} - 3 x ^{- 5} Please enter your answer as a fraction.

When using the property If $a = b$ , then $a ^ { n } = b ^ { n }$ , all potential solutions must be checked in the original equation.

Solve each equation. Match each equation with the corresponding solution. - $n = \frac { 121 } { 36 }$

Multiply and simplify where possible. Match each of the expressions with the expression to obtain a true statement. - $3,920$

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - $24 \sqrt { 6 }$

Use the distributive property to help simplify the expression. $2 \sqrt [ 3 ] { 3 } + 2 \sqrt [ 3 ] { 81 } - 2 \sqrt [ 3 ] { 24 }$

Solve the equation. $\sqrt { n - 18 } + \sqrt { n + 18 } = 2 \sqrt { n - 3 }$

Solve the equation. $3 \sqrt { m - 2 } = 7$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 128 y ^ { 3 } } { 49 x } }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 3 \sqrt { 4 x } + 3 \sqrt { 9 x } + 5 \sqrt { 16 x }$

Simplify the numerical expression. ( 4^-1) ^{- 2}

Solve the equation. $\sqrt { 7 x - 2 } - \sqrt { 2 x + 23 } = 0$

Solve the equation. $\sqrt [ 3 ] { 5 x - 3 } = \sqrt [ 3 ] { 2 - 4 x }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { 13 } ( \sqrt { 7 } + \sqrt { 3 } )$

Simplify. Express final results using positive exponents only. $\left( 5 y x ^ { \frac { 1 } { 4 } } \right) ^ { 4 }$

Find the indicated quotients. Express final results using positive integral exponents only. $\left( \frac { 28 x ^ { - 2 } y ^ { - 3 } } { 4 x ^ { 7 } y ^ { 8 } } \right) ^ { - 1 }$