Question 1

Subtract. $\left( 2 x ^ { 2 } y ^ { 3 } + 4 x y + 7 y ^ { 2 } \right) - \left( - 4 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)$

Accepted Answer

The answer of Subtract. \(\left( 2 x ^ { 2...

Question 2

Simplify the expression. $\left( b ^ { 8 } \right) ^ { 6 }$

Accepted Answer

A)  $b ^ { 48 }$ 
B)  $b ^ { 14 }$ 
C)  $\frac { 1 } { b ^ { 48 } }$ 
D)  $\frac { 1 } { b ^ { 2 } }$ 
E)  $\frac { 1 } { b ^ { 14 } }$ 
A)  $b ^ { 48 }$ 
B)  $b ^ { 14 }$ 
C)  $\frac { 1 } { b ^ { 48 } }$ 
D)  $\frac { 1 } { b ^ { 2 } }$ 
E)  $\frac { 1 } { b ^ { 14 } }$

Question 3

Perform the indicated operation: $\left( 4 c ^ { 4 } d - 7 c d + 8 c \right) + \left( 3 c d - 8 c ^ { 4 } d - 7 c \right)$

Accepted Answer

A)  $4 c ^ { 4 } d + 4 c d - c$ 
B)  $7 c ^ { 4 } d - c d + c$ 
C)  $- 4 c ^ { 8 } d ^ { 2 } - 4 c ^ { 2 } d ^ { 2 } + c ^ { 2 }$ 
D)  $- 4 c ^ { 4 } d - 4 c d + c$ 
A)  $4 c ^ { 4 } d + 4 c d - c$ 
B)  $7 c ^ { 4 } d - c d + c$ 
C)  $- 4 c ^ { 8 } d ^ { 2 } - 4 c ^ { 2 } d ^ { 2 } + c ^ { 2 }$ 
D)  $- 4 c ^ { 4 } d - 4 c d + c$

Question 4

Factor: $225 x ^ { 2 } + 169$

Accepted Answer

A)  $( 15 x + 13 ) ( 15 x - 13 )$ 
B)  $( 15 x + 13 ) ^ { 2 }$ 
C)  $( 15 x ) ^ { 2 } + ( 13 ) ^ { 2 }$ 
D)  prime 
A)  $( 15 x + 13 ) ( 15 x - 13 )$ 
B)  $( 15 x + 13 ) ^ { 2 }$ 
C)  $( 15 x ) ^ { 2 } + ( 13 ) ^ { 2 }$ 
D)  prime

Question 5

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. $7 ^ { 2 } r ^ { - 7 } \left( r ^ { 8 } \right) ^ { 5 }$

Accepted Answer

A)  $\frac { 49 } { r ^ { 33 } }$ 
B)  $49 r ^ { 6 }$ 
C)  $7 r ^ { 6 }$ 
D)  $7 r ^ { 47 }$ 
E)  $49 r ^ { 33 }$ 
A)  $\frac { 49 } { r ^ { 33 } }$ 
B)  $49 r ^ { 6 }$ 
C)  $7 r ^ { 6 }$ 
D)  $7 r ^ { 47 }$ 
E)  $49 r ^ { 33 }$

Question 6

Factor the expression completely. $- 21 x + 9 + 12 x ^ { 2 }$

Accepted Answer

A)  $( 7 x - 3 ) ( x - 1 )$ 
B)  $3 ( 4 x - 3 ) ( x - 1 )$ 
C)  $3 ( 7 x - 3 ) ( x - 1 )$ 
D)  $( 4 x - 3 ) ( 3 x - 1 )$ 
E)  prime 
A)  $( 7 x - 3 ) ( x - 1 )$ 
B)  $3 ( 4 x - 3 ) ( x - 1 )$ 
C)  $3 ( 7 x - 3 ) ( x - 1 )$ 
D)  $( 4 x - 3 ) ( 3 x - 1 )$ 
E)  prime

Question 7

Solve the equation. $y ^ { 2 } - 100 = 0$, y = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(y ^ { 2...

Question 8

The length of a rectangular ice-skating rink is 10 meters greater than twice its width. Find the width.

Accepted Answer

A)  28 m 
B)  25 m 
C)  29 m 
D)  30 m 
E)  31 m 
A)  28 m 
B)  25 m 
C)  29 m 
D)  30 m 
E)  31 m

Question 9

The approximate number of atoms of carbon in a $\frac { 1 } { 2 }$ -carat diamond can be found by computing the following expression. $\frac { 6.0 \times 10 ^ { 23 } } { 1.2 \times 10 ^ { 2 } }$ Express the number of carbon atoms in scientific and in standard notation.

Accepted Answer

A)  $5 \times 10 ^ { 22 } , 50,000,000,000,000,000,000$ 
B)  $5 \times 10 ^ { 21 } , 5,000,000,000,000,000,000,000$ 
C)  $5 \times 10 ^ { 21 } , 500,000,000,000,000,000,000$ 
D)  $5 \times 10 ^ { 11 } , 500,000,000,000$ 
E)  $5 \times 10 ^ { 19 } , 50,000,000,000,000,000,000$ 
A)  $5 \times 10 ^ { 22 } , 50,000,000,000,000,000,000$ 
B)  $5 \times 10 ^ { 21 } , 5,000,000,000,000,000,000,000$ 
C)  $5 \times 10 ^ { 21 } , 500,000,000,000,000,000,000$ 
D)  $5 \times 10 ^ { 11 } , 500,000,000,000$ 
E)  $5 \times 10 ^ { 19 } , 50,000,000,000,000,000,000$

Question 10

Multiply. Give the answer in scientific notation. $\left( 8.9 \times 10 ^ { - 5 } \right) \left( 5.3 \times 10 ^ { 12 } \right)$

Accepted Answer

A)  $4.717 \times 10 ^ { 7 }$ 
B)  $4.717 \times 10 ^ { 8 }$ 
C)  $5.057 \times 10 ^ { 7 }$ 
D)  $\text { 4. } 547 \times 10 ^ { 7 }$ 
E)  $4.887 \times 10 ^ { 8 }$ 
A)  $4.717 \times 10 ^ { 7 }$ 
B)  $4.717 \times 10 ^ { 8 }$ 
C)  $5.057 \times 10 ^ { 7 }$ 
D)  $\text { 4. } 547 \times 10 ^ { 7 }$ 
E)  $4.887 \times 10 ^ { 8 }$

Question 11

Simplify the expression. Write the answer using positive exponents. $4 ^ { - 2 }$

Accepted Answer

The answer of Simplify the expression. Write the answer using...

Question 12

Factor the expression completely. If the expression is prime, so indicate. $x ^ { 2 } + 4 x + 4 - y ^ { 2 }$

Accepted Answer

A)  $( x + 2 + y ) ( x + 2 - y )$ 
B)  $( x - 2 + y ) ( x - 2 - y )$ 
C)  $( x + 9 + y ) ( x + 9 - y )$ 
D)  $( x - 9 + y ) ( x - 9 - y )$ 
E)  prime 
A)  $( x + 2 + y ) ( x + 2 - y )$ 
B)  $( x - 2 + y ) ( x - 2 - y )$ 
C)  $( x + 9 + y ) ( x + 9 - y )$ 
D)  $( x - 9 + y ) ( x - 9 - y )$ 
E)  prime

Question 13

Multiply. $\left( 5 a ^ { 2 } b c ^ { 6 } \right) \left( - 4 a ^ { 3 } b ^ { 2 } c ^ { 3 } \right) \left( 5 a ^ { 4 } c ^ { 5 } \right)$

Accepted Answer

The answer of Multiply. \(\left( 5 a ^ { 2...

Question 14

Find a quadratic equation with solutions $\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }$ . Leave the answer in standard form with the smallest integer coefficients.

Accepted Answer

The answer of Find a quadratic equation with solutions \(\frac...

Question 15

Add. $\left( 3 a ^ { 2 } - 3 a - 6 \right) + \left( 5 a ^ { 2 } + 6 a + 1 \right)$

Accepted Answer

The answer of Add. \(\left( 3 a ^ { 2...

Question 16

Simplify the expression. Write the answer using positive exponents. $\left( \frac { 3 a ^ { 2 } b ^ { 4 } z ^ { - 3 } } { 2 a ^ { - 1 } b ^ { - 3 } z ^ { 5 } } \right) ^ { - 3 }$

Accepted Answer

The answer of Simplify the expression. Write the answer using...

Question 17

Perform the indicated operation: $( 9 x - 5 y ) ( 2 x + 6 y )$

Accepted Answer

A)  $18 x ^ { 2 } - 44 x y - 30 y ^ { 2 }$ 
B)  $18 x ^ { 2 } - 30 y ^ { 2 }$ 
C)  $18 x ^ { 2 } + 44 x y - 30 y ^ { 2 }$ 
D)  $18 x ^ { 2 } + 44 x y - 30 y$ 
A)  $18 x ^ { 2 } - 44 x y - 30 y ^ { 2 }$ 
B)  $18 x ^ { 2 } - 30 y ^ { 2 }$ 
C)  $18 x ^ { 2 } + 44 x y - 30 y ^ { 2 }$ 
D)  $18 x ^ { 2 } + 44 x y - 30 y$

Question 18

Factor the expression completely. $- 2 x ^ { 3 } + 16$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(- 2 x...

Question 19

Write 4,300,000 in scientific notation.

Accepted Answer

A)  $4.3 \times 10 ^ { - 6 }$ 
B)  $43 \times 10 ^ { 7 }$ 
C)  $4.3 \times 10 ^ { 6 }$ 
D)  $43 \times 10 ^ { - 7 }$ 
A)  $4.3 \times 10 ^ { - 6 }$ 
B)  $43 \times 10 ^ { 7 }$ 
C)  $4.3 \times 10 ^ { 6 }$ 
D)  $43 \times 10 ^ { - 7 }$

Question 20

Solve: $9 m ^ { 2 } = 4 m$

Accepted Answer

A)  $\left\{ \frac { 4 } { 9 } \right\}$ 
B)  $\left\{ 0 , \frac { 9 } { 4 } \right\}$ 
C)  $\left\{ 0 , \frac { 4 } { 9 } \right\}$ 
D)  $\left\{ 0 , - \frac { 4 } { 9 } \right\}$ 
A)  $\left\{ \frac { 4 } { 9 } \right\}$ 
B)  $\left\{ 0 , \frac { 9 } { 4 } \right\}$ 
C)  $\left\{ 0 , \frac { 4 } { 9 } \right\}$ 
D)  $\left\{ 0 , - \frac { 4 } { 9 } \right\}$

Subtract. $\left( 2 x ^ { 2 } y ^ { 3 } + 4 x y + 7 y ^ { 2 } \right) - \left( - 4 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)$

Simplify the expression. $\left( b ^ { 8 } \right) ^ { 6 }$

Perform the indicated operation: $\left( 4 c ^ { 4 } d - 7 c d + 8 c \right) + \left( 3 c d - 8 c ^ { 4 } d - 7 c \right)$

Factor: $225 x ^ { 2 } + 169$

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. $7 ^ { 2 } r ^ { - 7 } \left( r ^ { 8 } \right) ^ { 5 }$

Factor the expression completely. $- 21 x + 9 + 12 x ^ { 2 }$

Solve the equation. $y ^ { 2 } - 100 = 0$ , y = __________ If there is more than one solution, separate your answers with commas.

The length of a rectangular ice-skating rink is 10 meters greater than twice its width. Find the width.

The approximate number of atoms of carbon in a $\frac { 1 } { 2 }$ -carat diamond can be found by computing the following expression. $\frac { 6.0 \times 10 ^ { 23 } } { 1.2 \times 10 ^ { 2 } }$ Express the number of carbon atoms in scientific and in standard notation.

Multiply. Give the answer in scientific notation. $\left( 8.9 \times 10 ^ { - 5 } \right) \left( 5.3 \times 10 ^ { 12 } \right)$

Simplify the expression. Write the answer using positive exponents. $4 ^ { - 2 }$

Factor the expression completely. If the expression is prime, so indicate. $x ^ { 2 } + 4 x + 4 - y ^ { 2 }$

Multiply. $\left( 5 a ^ { 2 } b c ^ { 6 } \right) \left( - 4 a ^ { 3 } b ^ { 2 } c ^ { 3 } \right) \left( 5 a ^ { 4 } c ^ { 5 } \right)$

Find a quadratic equation with solutions $\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }$ . Leave the answer in standard form with the smallest integer coefficients.

Add. $\left( 3 a ^ { 2 } - 3 a - 6 \right) + \left( 5 a ^ { 2 } + 6 a + 1 \right)$

Simplify the expression. Write the answer using positive exponents. $\left( \frac { 3 a ^ { 2 } b ^ { 4 } z ^ { - 3 } } { 2 a ^ { - 1 } b ^ { - 3 } z ^ { 5 } } \right) ^ { - 3 }$

Perform the indicated operation: $( 9 x - 5 y ) ( 2 x + 6 y )$

Factor the expression completely. $- 2 x ^ { 3 } + 16$ If the expression is prime, so indicate.

Write 4,300,000 in scientific notation.

Solve: $9 m ^ { 2 } = 4 m$

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

Subtract. (2x2y3+4xy+7y2)−(−4x2y3−2xy+5y2+y)\left( 2 x ^ { 2 } y ^ { 3 } + 4 x y + 7 y ^ { 2 } \right) - \left( - 4 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)(2x2y3+4xy+7y2)−(−4x2y3−2xy+5y2+y)

Simplify the expression. (b8)6\left( b ^ { 8 } \right) ^ { 6 }(b8)6

Perform the indicated operation: (4c4d−7cd+8c)+(3cd−8c4d−7c)\left( 4 c ^ { 4 } d - 7 c d + 8 c \right) + \left( 3 c d - 8 c ^ { 4 } d - 7 c \right)(4c4d−7cd+8c)+(3cd−8c4d−7c)

Factor: 225x2+169225 x ^ { 2 } + 169225x2+169

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. 72r−7(r8)57 ^ { 2 } r ^ { - 7 } \left( r ^ { 8 } \right) ^ { 5 }72r−7(r8)5

Factor the expression completely. −21x+9+12x2- 21 x + 9 + 12 x ^ { 2 }−21x+9+12x2

Solve the equation. y2−100=0y ^ { 2 } - 100 = 0y2−100=0 , y = __________ If there is more than one solution, separate your answers with commas.

The length of a rectangular ice-skating rink is 10 meters greater than twice its width. Find the width.

Multiply. Give the answer in scientific notation. (8.9×10−5)(5.3×1012)\left( 8.9 \times 10 ^ { - 5 } \right) \left( 5.3 \times 10 ^ { 12 } \right)(8.9×10−5)(5.3×1012)

Simplify the expression. Write the answer using positive exponents. 4−24 ^ { - 2 }4−2

Factor the expression completely. If the expression is prime, so indicate. x2+4x+4−y2x ^ { 2 } + 4 x + 4 - y ^ { 2 }x2+4x+4−y2

Multiply. (5a2bc6)(−4a3b2c3)(5a4c5)\left( 5 a ^ { 2 } b c ^ { 6 } \right) \left( - 4 a ^ { 3 } b ^ { 2 } c ^ { 3 } \right) \left( 5 a ^ { 4 } c ^ { 5 } \right)(5a2bc6)(−4a3b2c3)(5a4c5)

Find a quadratic equation with solutions 35 and −52\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }53​ and −25​ . Leave the answer in standard form with the smallest integer coefficients.

Add. (3a2−3a−6)+(5a2+6a+1)\left( 3 a ^ { 2 } - 3 a - 6 \right) + \left( 5 a ^ { 2 } + 6 a + 1 \right)(3a2−3a−6)+(5a2+6a+1)

Simplify the expression. Write the answer using positive exponents. (3a2b4z−32a−1b−3z5)−3\left( \frac { 3 a ^ { 2 } b ^ { 4 } z ^ { - 3 } } { 2 a ^ { - 1 } b ^ { - 3 } z ^ { 5 } } \right) ^ { - 3 }(2a−1b−3z53a2b4z−3​)−3

Perform the indicated operation: (9x−5y)(2x+6y)( 9 x - 5 y ) ( 2 x + 6 y )(9x−5y)(2x+6y)

Factor the expression completely. −2x3+16- 2 x ^ { 3 } + 16−2x3+16 If the expression is prime, so indicate.

Write 4,300,000 in scientific notation.

Solve: 9m2=4m9 m ^ { 2 } = 4 m9m2=4m

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

Subtract. $\left( 2 x ^ { 2 } y ^ { 3 } + 4 x y + 7 y ^ { 2 } \right) - \left( - 4 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)$

Simplify the expression. $\left( b ^ { 8 } \right) ^ { 6 }$

Perform the indicated operation: $\left( 4 c ^ { 4 } d - 7 c d + 8 c \right) + \left( 3 c d - 8 c ^ { 4 } d - 7 c \right)$

Factor: $225 x ^ { 2 } + 169$

Simplify the expression. Assume that the variable represents a nonzero real number. Write the answer using a positive exponent only. $7 ^ { 2 } r ^ { - 7 } \left( r ^ { 8 } \right) ^ { 5 }$

Factor the expression completely. $- 21 x + 9 + 12 x ^ { 2 }$

Solve the equation. $y ^ { 2 } - 100 = 0$ , y = __________ If there is more than one solution, separate your answers with commas.

Multiply. Give the answer in scientific notation. $\left( 8.9 \times 10 ^ { - 5 } \right) \left( 5.3 \times 10 ^ { 12 } \right)$

Simplify the expression. Write the answer using positive exponents. $4 ^ { - 2 }$

Factor the expression completely. If the expression is prime, so indicate. $x ^ { 2 } + 4 x + 4 - y ^ { 2 }$

Multiply. $\left( 5 a ^ { 2 } b c ^ { 6 } \right) \left( - 4 a ^ { 3 } b ^ { 2 } c ^ { 3 } \right) \left( 5 a ^ { 4 } c ^ { 5 } \right)$

Find a quadratic equation with solutions $\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }$ . Leave the answer in standard form with the smallest integer coefficients.

Add. $\left( 3 a ^ { 2 } - 3 a - 6 \right) + \left( 5 a ^ { 2 } + 6 a + 1 \right)$

Simplify the expression. Write the answer using positive exponents. $\left( \frac { 3 a ^ { 2 } b ^ { 4 } z ^ { - 3 } } { 2 a ^ { - 1 } b ^ { - 3 } z ^ { 5 } } \right) ^ { - 3 }$

Perform the indicated operation: $( 9 x - 5 y ) ( 2 x + 6 y )$

Factor the expression completely. $- 2 x ^ { 3 } + 16$ If the expression is prime, so indicate.

Solve: $9 m ^ { 2 } = 4 m$