Question 1

Multiply. $3 x ^ { 2 } y z \left( x ^ { 2 } - 4 y + 3 z ^ { 2 } \right)$

Accepted Answer

A)  $3 x ^ { 4 } y z - 12 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 3 }$ 
B)  $3 x ^ { 5 } y z - 13 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 4 }$ 
C)  $3 x ^ { 4 } y z - 12 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 2 }$ 
D)  $3 x ^ { 5 } y z - 12 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 2 }$ 
E)  $3 x ^ { 5 } y z - 14 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 3 }$ 
A)  $3 x ^ { 4 } y z - 12 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 3 }$ 
B)  $3 x ^ { 5 } y z - 13 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 4 }$ 
C)  $3 x ^ { 4 } y z - 12 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 2 }$ 
D)  $3 x ^ { 5 } y z - 12 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 2 }$ 
E)  $3 x ^ { 5 } y z - 14 x ^ { 2 } y ^ { 2 } z + 9 x ^ { 2 } y z ^ { 3 }$

Question 2

2,500 is written in _________ form.

Accepted Answer

The answer of 2,500 is written in _________ form....

Question 3

Simplify: $\left( \frac { 3 x y ^ { - 3 } } { 2 x ^ { - 4 } y ^ { 4 } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 9 } { 4 x ^ { 6 } y ^ { 14 } }$ 
B)  $\frac { 3 x ^ { 10 } } { 2 y ^ { 14 } }$ 
C)  $\frac { 9 x ^ { 10 } } { 4 y ^ { 14 } }$ 
D)  $\frac { 4 } { 9 x ^ { 6 } y ^ { 9 } }$ 
A)  $\frac { 9 } { 4 x ^ { 6 } y ^ { 14 } }$ 
B)  $\frac { 3 x ^ { 10 } } { 2 y ^ { 14 } }$ 
C)  $\frac { 9 x ^ { 10 } } { 4 y ^ { 14 } }$ 
D)  $\frac { 4 } { 9 x ^ { 6 } y ^ { 9 } }$

Question 4

Factor the expression completely. $625 x ^ { 4 } - 16 y ^ { 4 }$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(625 x ^...

Question 5

Solve the equation. $y ^ { 3 } - 49 y = 0$,  y = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(y ^ { 3...

Question 6

Simplify: $\left( a ^ { 4 } \right) ^ { - 2 } \cdot \left( 3 a ^ { 3 } \right) ^ { 3 }$

Accepted Answer

A)  $27 a$ 
B)  $\frac { 27 } { a }$ 
C)  $9a$ 
D)  27 
A)  $27 a$ 
B)  $\frac { 27 } { a }$ 
C)  $9a$ 
D)  27

Question 7

Simplify the expression. $\left( r ^ { 5 } s \right) ^ { 2 }$

Accepted Answer

A)  $r ^ { 7 } s ^ { 3 }$ 
B)  $\frac { r ^ { 10 } } { s ^ { 2 } }$ 
C)  $r ^ { 5 } s ^ { 2 }$ 
D)  $r ^ { 10 } s ^ { 3 }$ 
E)  $r ^ { 10 } s ^ { 2 }$ 
A)  $r ^ { 7 } s ^ { 3 }$ 
B)  $\frac { r ^ { 10 } } { s ^ { 2 } }$ 
C)  $r ^ { 5 } s ^ { 2 }$ 
D)  $r ^ { 10 } s ^ { 3 }$ 
E)  $r ^ { 10 } s ^ { 2 }$

Question 8

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. $2 ^ { 2 } r ^ { - 5 } \left( r ^ { 9 } \right) ^ { 2 }$

Accepted Answer

The answer of Simplify the expression. Assume that the variable...

Question 9

Factor the expression completely. $6 x ^ { 2 } - 49 - 7 x$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(6 x ^...

Question 10

Simplify the expression. $4 ^ { - 4 }$

Accepted Answer

A)  -16 
B)  -256 
C)  256 
D)  $- \frac { 1 } { 256 }$ 
E)  $\frac { 1 } { 256 }$ 
A)  -16 
B)  -256 
C)  256 
D)  $- \frac { 1 } { 256 }$ 
E)  $\frac { 1 } { 256 }$

Question 11

Factor, if possible. $6 y ^ { 2 } + 3 y$

Accepted Answer

A)  $( 3 y + 2 ) ( 2 y + 1 )$ 
B)  $3 y ^ { 2 } ( 2 + y )$ 
C)  $3 y ( 2 y + 1 )$ 
D)  $3 \left( 2 y ^ { 2 } + y \right)$ 
E)  $\text { prime }$ 
A)  $( 3 y + 2 ) ( 2 y + 1 )$ 
B)  $3 y ^ { 2 } ( 2 + y )$ 
C)  $3 y ( 2 y + 1 )$ 
D)  $3 \left( 2 y ^ { 2 } + y \right)$ 
E)  $\text { prime }$

Question 12

Factor completely: $x ^ { 3 } - 25 x - 3 x ^ { 2 } + 75$

Accepted Answer

A)  $( x - 3 ) ( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 25 \right)$ 
B)  $( x + 3 ) ( x - 5 ) ( x + 5 )$ 
C)  $( x - 3 ) ( x - 5 ) ( x + 5 )$ 
D)  $( x - 3 ) \left( x ^ { 2 } - 25 \right)$ 
A)  $( x - 3 ) ( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 25 \right)$ 
B)  $( x + 3 ) ( x - 5 ) ( x + 5 )$ 
C)  $( x - 3 ) ( x - 5 ) ( x + 5 )$ 
D)  $( x - 3 ) \left( x ^ { 2 } - 25 \right)$

Question 13

What is the reciprocal of the opposite of $3.2 \times 10 ^ { - 3 }$ ?
 Write the answer in scientific notation.

Accepted Answer

The answer of What is the reciprocal of the opposite...

Question 14

Factor completely: $- 6 x ^ { 2 } + 18 x + 60$

Accepted Answer

A)  $- 6 \left( x ^ { 2 } - 3 x + 10 \right)$ 
B)  $- 6 \left( x ^ { 2 } + 3 x + 10 \right)$ 
C)  $- 6 ( x + 5 ) ( x - 2 )$ 
D)  $- 6 ( x - 5 ) ( x + 2 )$ 
A)  $- 6 \left( x ^ { 2 } - 3 x + 10 \right)$ 
B)  $- 6 \left( x ^ { 2 } + 3 x + 10 \right)$ 
C)  $- 6 ( x + 5 ) ( x - 2 )$ 
D)  $- 6 ( x - 5 ) ( x + 2 )$

Question 15

Factor: $3 a ^ { 2 n } + 9 a ^ { n } - 30$ Assume that n is a natural number.

Accepted Answer

The answer of Factor: \(3 a ^ { 2 n...

Question 16

A(n) _________ equation is any equation that can be written in the form $a x ^ { 2 } + b x + c = 0 , \text { where } a \neq 0$ .

Accepted Answer

The answer of A(n) _________ equation is any equation that...

Question 17

Solve the equation. $( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1$, x = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(( x + 7...

Question 18

Simplify the expression. $x ^ { 5 } x ^ { 14 } x$

Accepted Answer

A)  $x ^ { 20 }$ 
B)  $x ^ { 19 }$ 
C)  $x ^ { 18 }$ 
D)  $x ^ { 22 }$ 
E)  $x ^ { 21 }$ 
A)  $x ^ { 20 }$ 
B)  $x ^ { 19 }$ 
C)  $x ^ { 18 }$ 
D)  $x ^ { 22 }$ 
E)  $x ^ { 21 }$

Question 19

Simplify the expression. $\left( r ^ { 7 } s \right) ^ { 4 }$

Accepted Answer

The answer of Simplify the expression. \(\left( r ^ {...

Question 20

Divide. Give the answer in scientific notation. $\frac { 3.48 \times 10 ^ { - 13 } } { 8.7 \times 10 ^ { - 6 } }$  $\times 10 ^ { - }$

Accepted Answer

The answer of Divide. Give the answer in scientific notation....

Multiply. $3 x ^ { 2 } y z \left( x ^ { 2 } - 4 y + 3 z ^ { 2 } \right)$

2,500 is written in _________ form.

Simplify: $\left( \frac { 3 x y ^ { - 3 } } { 2 x ^ { - 4 } y ^ { 4 } } \right) ^ { 2 }$

Factor the expression completely. $625 x ^ { 4 } - 16 y ^ { 4 }$ If the expression is prime, so indicate.

Solve the equation. $y ^ { 3 } - 49 y = 0$ , y = __________ If there is more than one solution, separate your answers with commas.

Simplify: $\left( a ^ { 4 } \right) ^ { - 2 } \cdot \left( 3 a ^ { 3 } \right) ^ { 3 }$

Simplify the expression. $\left( r ^ { 5 } s \right) ^ { 2 }$

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. $2 ^ { 2 } r ^ { - 5 } \left( r ^ { 9 } \right) ^ { 2 }$

Factor the expression completely. $6 x ^ { 2 } - 49 - 7 x$ If the expression is prime, so indicate.

Simplify the expression. $4 ^ { - 4 }$

Factor, if possible. $6 y ^ { 2 } + 3 y$

Factor completely: $x ^ { 3 } - 25 x - 3 x ^ { 2 } + 75$

What is the reciprocal of the opposite of $3.2 \times 10 ^ { - 3 }$ ? Write the answer in scientific notation.

Factor completely: $- 6 x ^ { 2 } + 18 x + 60$

Factor: $3 a ^ { 2 n } + 9 a ^ { n } - 30$ Assume that n is a natural number.

A(n) _________ equation is any equation that can be written in the form $a x ^ { 2 } + b x + c = 0 , \text { where } a \neq 0$ .

Solve the equation. $( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1$ , x = __________ If there is more than one solution, separate your answers with commas.

Simplify the expression. $x ^ { 5 } x ^ { 14 } x$

Simplify the expression. $\left( r ^ { 7 } s \right) ^ { 4 }$

Divide. Give the answer in scientific notation. $\frac { 3.48 \times 10 ^ { - 13 } } { 8.7 \times 10 ^ { - 6 } }$ $Divide. Give the answer in scientific notation. \frac { 3.48 \times 10 ^ { - 13 } } { 8.7 \times 10 ^ { - 6 } } \times 10 ^ { - }$ $\times 10 ^ { - }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 5: Exponents, Polynomials, and Polynomial Functions

Multiply. 3x2yz(x2−4y+3z2)3 x ^ { 2 } y z \left( x ^ { 2 } - 4 y + 3 z ^ { 2 } \right)3x2yz(x2−4y+3z2)

2,500 is written in _________ form.

Simplify: (3xy−32x−4y4)2\left( \frac { 3 x y ^ { - 3 } } { 2 x ^ { - 4 } y ^ { 4 } } \right) ^ { 2 }(2x−4y43xy−3​)2

Factor the expression completely. 625x4−16y4625 x ^ { 4 } - 16 y ^ { 4 }625x4−16y4 If the expression is prime, so indicate.

Solve the equation. y3−49y=0y ^ { 3 } - 49 y = 0y3−49y=0 , y = __________ If there is more than one solution, separate your answers with commas.

Simplify: (a4)−2⋅(3a3)3\left( a ^ { 4 } \right) ^ { - 2 } \cdot \left( 3 a ^ { 3 } \right) ^ { 3 }(a4)−2⋅(3a3)3

Simplify the expression. (r5s)2\left( r ^ { 5 } s \right) ^ { 2 }(r5s)2

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. 22r−5(r9)22 ^ { 2 } r ^ { - 5 } \left( r ^ { 9 } \right) ^ { 2 }22r−5(r9)2

Factor the expression completely. 6x2−49−7x6 x ^ { 2 } - 49 - 7 x6x2−49−7x If the expression is prime, so indicate.

Simplify the expression. 4−44 ^ { - 4 }4−4

Factor, if possible. 6y2+3y6 y ^ { 2 } + 3 y6y2+3y

Factor completely: x3−25x−3x2+75x ^ { 3 } - 25 x - 3 x ^ { 2 } + 75x3−25x−3x2+75

What is the reciprocal of the opposite of 3.2×10−33.2 \times 10 ^ { - 3 }3.2×10−3 ? Write the answer in scientific notation.

Factor completely: −6x2+18x+60- 6 x ^ { 2 } + 18 x + 60−6x2+18x+60

Factor: 3a2n+9an−303 a ^ { 2 n } + 9 a ^ { n } - 303a2n+9an−30 Assume that n is a natural number.

A(n) _________ equation is any equation that can be written in the form ax2+bx+c=0, where a≠0a x ^ { 2 } + b x + c = 0 , \text { where } a \neq 0ax2+bx+c=0, where a=0 .

Solve the equation. (x+7)2=−2(x+7)−1( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1(x+7)2=−2(x+7)−1 , x = __________ If there is more than one solution, separate your answers with commas.

Simplify the expression. x5x14xx ^ { 5 } x ^ { 14 } xx5x14x

Simplify the expression. (r7s)4\left( r ^ { 7 } s \right) ^ { 4 }(r7s)4

Divide. Give the answer in scientific notation. 3.48×10−138.7×10−6\frac { 3.48 \times 10 ^ { - 13 } } { 8.7 \times 10 ^ { - 6 } }8.7×10−63.48×10−13​ ×10−\times 10 ^ { - }×10−

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Multiply. $3 x ^ { 2 } y z \left( x ^ { 2 } - 4 y + 3 z ^ { 2 } \right)$

Simplify: $\left( \frac { 3 x y ^ { - 3 } } { 2 x ^ { - 4 } y ^ { 4 } } \right) ^ { 2 }$

Factor the expression completely. $625 x ^ { 4 } - 16 y ^ { 4 }$ If the expression is prime, so indicate.

Solve the equation. $y ^ { 3 } - 49 y = 0$ , y = __________ If there is more than one solution, separate your answers with commas.

Simplify: $\left( a ^ { 4 } \right) ^ { - 2 } \cdot \left( 3 a ^ { 3 } \right) ^ { 3 }$

Simplify the expression. $\left( r ^ { 5 } s \right) ^ { 2 }$

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. $2 ^ { 2 } r ^ { - 5 } \left( r ^ { 9 } \right) ^ { 2 }$

Factor the expression completely. $6 x ^ { 2 } - 49 - 7 x$ If the expression is prime, so indicate.

Simplify the expression. $4 ^ { - 4 }$

Factor, if possible. $6 y ^ { 2 } + 3 y$

Factor completely: $x ^ { 3 } - 25 x - 3 x ^ { 2 } + 75$

What is the reciprocal of the opposite of $3.2 \times 10 ^ { - 3 }$ ? Write the answer in scientific notation.

Factor completely: $- 6 x ^ { 2 } + 18 x + 60$

Factor: $3 a ^ { 2 n } + 9 a ^ { n } - 30$ Assume that n is a natural number.

A(n) _________ equation is any equation that can be written in the form $a x ^ { 2 } + b x + c = 0 , \text { where } a \neq 0$ .

Solve the equation. $( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1$ , x = __________ If there is more than one solution, separate your answers with commas.

Simplify the expression. $x ^ { 5 } x ^ { 14 } x$

Simplify the expression. $\left( r ^ { 7 } s \right) ^ { 4 }$

Divide. Give the answer in scientific notation. $\frac { 3.48 \times 10 ^ { - 13 } } { 8.7 \times 10 ^ { - 6 } }$ $Divide. Give the answer in scientific notation. \frac { 3.48 \times 10 ^ { - 13 } } { 8.7 \times 10 ^ { - 6 } } \times 10 ^ { - }$ $\times 10 ^ { - }$