Question 1

Write in decimal notation.
-$1.77 \times 10 ^ { - 4 }$

Accepted Answer

A)  $- 177,000$ 
B)  $0.00177$ 
C)  $0.0000177$ 
D)  $0.000177$ 
A)  $- 177,000$ 
B)  $0.00177$ 
C)  $0.0000177$ 
D)  $0.000177$

Question 2

Solve the problem.
-$$12 x ^ { 5 } \left( - 8 x ^ { 6 } + 3 x ^ { 4 } + 11 \right)$$

Accepted Answer

A)  $- 96 x ^ { 11 } + 36 x ^ { 9 }$ 
B)  $- 96 x ^ { 11 } + 3 x ^ { 4 } + 11$ 
C)  $- 96 x ^ { 6 } + 36 x ^ { 4 } + 132$ 
D)  $- 96 x ^ { 11 } + 36 x ^ { 9 } + 132 x ^ { 5 }$ 
A)  $- 96 x ^ { 11 } + 36 x ^ { 9 }$ 
B)  $- 96 x ^ { 11 } + 3 x ^ { 4 } + 11$ 
C)  $- 96 x ^ { 6 } + 36 x ^ { 4 } + 132$ 
D)  $- 96 x ^ { 11 } + 36 x ^ { 9 } + 132 x ^ { 5 }$

Question 3

Multiply and leave your answer in exponent form.
-$( 7 x ) \left( 8 x ^ { 5 } \right) \left( x ^ { 7 } \right)$

Accepted Answer

A)  $56 \mathrm { x } ^ { 12 }$ 
B)  $15 x ^ { 12 }$ 
C)  $56 x ^ { 13 }$ 
D)  $16 \mathrm { x } ^ { 13 }$ 
A)  $56 \mathrm { x } ^ { 12 }$ 
B)  $15 x ^ { 12 }$ 
C)  $56 x ^ { 13 }$ 
D)  $16 \mathrm { x } ^ { 13 }$

Question 4

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { 12 m ^ { 3 } n ^ { 10 } } { 4 m ^ { 2 } n ^ { 7 } }$

Accepted Answer

A)  $3 n ^ { 3 }$ 
B)  $3 m n ^ { 3 }$ 
C)  $12 \mathrm { mn } ^ { 3 }$ 
D)  $3 m ^ { 5 } n$ 
A)  $3 n ^ { 3 }$ 
B)  $3 m n ^ { 3 }$ 
C)  $12 \mathrm { mn } ^ { 3 }$ 
D)  $3 m ^ { 5 } n$

Question 5

Solve the problem.
-$$\frac { 1 } { 4 } x ^ { 4 } y ^ { 6 } ( 3 x - 10 y + 8 )$$

Accepted Answer

A)  $\frac { 3 } { 4 } x ^ { 5 } y ^ { 6 } - \frac { 5 } { 2 } x ^ { 5 } y ^ { 7 } + 2 x ^ { 4 } y ^ { 6 }$ 
B)  $\frac { 3 } { 4 } x ^ { 5 } y ^ { 6 } - \frac { 5 } { 2 } x ^ { 4 } y ^ { 7 } + 2 x ^ { 4 } y ^ { 6 }$ 
C)  $\frac { 3 } { 4 } x ^ { 5 } y ^ { 6 } - \frac { 5 } { 2 } x ^ { 4 } y ^ { 7 } + 2$ 
D)  $\frac { 1 } { 4 } x ^ { 4 } y ^ { 6 }$ 
A)  $\frac { 3 } { 4 } x ^ { 5 } y ^ { 6 } - \frac { 5 } { 2 } x ^ { 5 } y ^ { 7 } + 2 x ^ { 4 } y ^ { 6 }$ 
B)  $\frac { 3 } { 4 } x ^ { 5 } y ^ { 6 } - \frac { 5 } { 2 } x ^ { 4 } y ^ { 7 } + 2 x ^ { 4 } y ^ { 6 }$ 
C)  $\frac { 3 } { 4 } x ^ { 5 } y ^ { 6 } - \frac { 5 } { 2 } x ^ { 4 } y ^ { 7 } + 2$ 
D)  $\frac { 1 } { 4 } x ^ { 4 } y ^ { 6 }$

Question 6

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$$\left( \frac { 3 x ^ { 2 } y ^ { 3 } } { z ^ { 4 } } \right) ^ { 3 }$$

Accepted Answer

A)  $\frac { 3 x ^ { 6 } y ^ { 9 } } { z ^ { 7 } }$ 
B)  $\frac { 3 x ^ { 6 } y ^ { 9 } } { z ^ { 12 } }$ 
C)  $\frac { 27 x ^ { 6 } y ^ { 9 } } { z ^ { 12 } }$ 
D)  $\frac { 27 x ^ { 5 } y ^ { 6 } } { z ^ { 7 } }$ 
A)  $\frac { 3 x ^ { 6 } y ^ { 9 } } { z ^ { 7 } }$ 
B)  $\frac { 3 x ^ { 6 } y ^ { 9 } } { z ^ { 12 } }$ 
C)  $\frac { 27 x ^ { 6 } y ^ { 9 } } { z ^ { 12 } }$ 
D)  $\frac { 27 x ^ { 5 } y ^ { 6 } } { z ^ { 7 } }$

Question 7

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
-$\left( \frac { x y ^ { 5 } } { x ^ { 6 } y } \right) ^ { - 2 }$

Accepted Answer

A)  $\frac { y ^ { 8 } } { x ^ { 10 } }$ 
B)  $\frac { x ^ { 10 } } { y ^ { 8 } }$ 
C)  $\frac { 1 } { x ^ { 14 } y ^ { 12 } }$ 
D)  $\frac { 1 } { x ^ { 8 } y ^ { 11 } }$ 
A)  $\frac { y ^ { 8 } } { x ^ { 10 } }$ 
B)  $\frac { x ^ { 10 } } { y ^ { 8 } }$ 
C)  $\frac { 1 } { x ^ { 14 } y ^ { 12 } }$ 
D)  $\frac { 1 } { x ^ { 8 } y ^ { 11 } }$

Question 8

Perform the indicated operations.
-$$( 3 x - 8 ) + ( 6 x - 9 )$$

Accepted Answer

A)  $9 x - 17$ 
B)  $- 8 x$ 
C)  $9 x$ 
D)  $9 x ^ { 2 } - 17$ 
A)  $9 x - 17$ 
B)  $- 8 x$ 
C)  $9 x$ 
D)  $9 x ^ { 2 } - 17$

Question 9

Solve.
-If the mass of an object is $4.61825 \times 10 ^ { - 5 }$ tons and its volume is $7.25 \times 10 ^ { - 3 }$ cubic feet, find the density of this object. (Use the formula $D = \frac { M } { V }$ and round to the nearest hundredth, if necessary.)

Accepted Answer

A)  $6.37 \times 10 ^ { - 2 }$ tons per cubic foot 
B)  $6.37 \times 10 ^ { - 3 }$ tons per cubic foot 
C)  $6.37 \times 10 ^ { - 4 }$ tons per cubic foot 
D)  $63.7 \times 10 ^ { - 3 }$ tons per cubic foot 
A)  $6.37 \times 10 ^ { - 2 }$ tons per cubic foot 
B)  $6.37 \times 10 ^ { - 3 }$ tons per cubic foot 
C)  $6.37 \times 10 ^ { - 4 }$ tons per cubic foot 
D)  $63.7 \times 10 ^ { - 3 }$ tons per cubic foot

Question 10

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$\frac { ( 5,000,000 ) ( 78,000 ) } { 39,000,000,000 }$

Accepted Answer

A)  $1.0$ 
B)  $1.0 \times 10 ^ { 1 }$ 
C)  $1.0 \times 10 ^ { - 1 }$ 
D)  $1.0 \times 2$ 
A)  $1.0$ 
B)  $1.0 \times 10 ^ { 1 }$ 
C)  $1.0 \times 10 ^ { - 1 }$ 
D)  $1.0 \times 2$

Question 11

Solve
-

Accepted Answer

A)   
B)   
C)   
D)   
A)   
B)   
C)   
D)

Question 12

Multiply and leave your answer in exponent form.
-$$\left( x ^ { 3 } \right) \left( x ^ { 4 } \right)$$

Accepted Answer

A)  $( 2 x ) ^ { 7 }$ 
B)  $x ^ { 7 }$ 
C) 2x7 
D)  $x ^ { 12 }$ 
A)  $( 2 x ) ^ { 7 }$ 
B)  $x ^ { 7 }$ 
C) 2x7 
D)  $x ^ { 12 }$

Question 13

Write in decimal notation.
-$$9.254 \times 10 ^ { - 6 }$$

Accepted Answer

A)  $0.000009254$ 
B)  $- 9,254,000$ 
C)  $0.00009254$ 
D)  $0.0000009254$ 
A)  $0.000009254$ 
B)  $- 9,254,000$ 
C)  $0.00009254$ 
D)  $0.0000009254$

Question 14

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$( - 3 x y ) ^ { 4 }$

Accepted Answer

A)  $81 x y$ 
B)  $- 12 x ^ { 4 } y ^ { 4 }$ 
C)  $81 x ^ { 4 } y ^ { 4 }$ 
D)  $- 12 x y$ 
A)  $81 x y$ 
B)  $- 12 x ^ { 4 } y ^ { 4 }$ 
C)  $81 x ^ { 4 } y ^ { 4 }$ 
D)  $- 12 x y$

Question 15

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$$( 180,000,000 ) ( 0.00003 ) ( 2000 ) ( 0.003 )$$

Accepted Answer

A)  $3.24 \times 10 ^ { 5 }$ 
B)  $3.24 \times 10 ^ { 6 }$ 
C)  $3.24 \times 10 ^ { 3 }$ 
D)  $3.24 \times 10 ^ { 4 }$ 
A)  $3.24 \times 10 ^ { 5 }$ 
B)  $3.24 \times 10 ^ { 6 }$ 
C)  $3.24 \times 10 ^ { 3 }$ 
D)  $3.24 \times 10 ^ { 4 }$

Question 16

Solve the problem.
-The lengths and the widths of the following two rectangles are labeled. Create a polynomial that describes the sum of the area of these two rectangles.

Accepted Answer

A)  $10 x + 8$ 
B)  $4 x - 2$ 
C)  $2 x - 2$ 
D)  $10 x - 2$ 
A)  $10 x + 8$ 
B)  $4 x - 2$ 
C)  $2 x - 2$ 
D)  $10 x - 2$

Question 17

Perform the indicated operations.
-$$\left( 7 x ^ { 2 } + 13 x + 15 \right) + \left( - 5 x ^ { 2 } + 6 x - 9 \right)$$

Accepted Answer

A)  $x ^ { 2 } + 19 x + 6$ 
B)  $x ^ { 2 } - 19 x + 6$ 
C)  $x ^ { 2 } + 18 x + 24$ 
D)  $x ^ { 2 } + 19 x + 24$ 
A)  $x ^ { 2 } + 19 x + 6$ 
B)  $x ^ { 2 } - 19 x + 6$ 
C)  $x ^ { 2 } + 18 x + 24$ 
D)  $x ^ { 2 } + 19 x + 24$

Question 18

Solve the problem.
-$( x - 8 y ) ( x - 5 y )$

Accepted Answer

A)  $x ^ { 2 } - 13 x y + 40 y ^ { 2 }$ 
B)  $x ^ { 2 } - 16 x y + 40 y ^ { 2 }$ 
C)  $x ^ { 2 } - 13 x y - 13 y ^ { 2 }$ 
D)  $x - 13 x y + 40 y$ 
A)  $x ^ { 2 } - 13 x y + 40 y ^ { 2 }$ 
B)  $x ^ { 2 } - 16 x y + 40 y ^ { 2 }$ 
C)  $x ^ { 2 } - 13 x y - 13 y ^ { 2 }$ 
D)  $x - 13 x y + 40 y$

Question 19

Solve.
-Approximately $7 \times 10 ^ { 3 }$ employees of a certain company average $\$ 30,000$ each year in salary. What is the total amount earned by all the employees of this company per year? Write your answer in scientific notation.

Accepted Answer

A)  $\$ 21 \times 10 ^ { 9 }$ 
B)  $\$ 21 \times 10 ^ { 8 }$ 
C)  $\$ 2.1 \times 10 ^ { 9 }$ 
D)  $\$ 2.1 \times 10 ^ { 8 }$ 
A)  $\$ 21 \times 10 ^ { 9 }$ 
B)  $\$ 21 \times 10 ^ { 8 }$ 
C)  $\$ 2.1 \times 10 ^ { 9 }$ 
D)  $\$ 2.1 \times 10 ^ { 8 }$

Question 20

Write in simplest exponent form.
-x · x · x · x

Accepted Answer

A)  $4 x$ 
B)  $4 ^ { x }$ 
C)  4 
D)  $x ^ { 4 }$ 
A)  $4 x$ 
B)  $4 ^ { x }$ 
C)  4 
D)  $x ^ { 4 }$

Write in decimal notation. - $1.77 \times 10 ^ { - 4 }$

Solve the problem. - $12 x ^ { 5 } \left( - 8 x ^ { 6 } + 3 x ^ { 4 } + 11 \right)$

Multiply and leave your answer in exponent form. - $( 7 x ) \left( 8 x ^ { 5 } \right) \left( x ^ { 7 } \right)$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { 12 m ^ { 3 } n ^ { 10 } } { 4 m ^ { 2 } n ^ { 7 } }$

Solve the problem. - $\frac { 1 } { 4 } x ^ { 4 } y ^ { 6 } ( 3 x - 10 y + 8 )$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\left( \frac { 3 x ^ { 2 } y ^ { 3 } } { z ^ { 4 } } \right) ^ { 3 }$

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - $\left( \frac { x y ^ { 5 } } { x ^ { 6 } y } \right) ^ { - 2 }$

Perform the indicated operations. - $( 3 x - 8 ) + ( 6 x - 9 )$

Solve. -If the mass of an object is $4.61825 \times 10 ^ { - 5 }$ tons and its volume is $7.25 \times 10 ^ { - 3 }$ cubic feet, find the density of this object. (Use the formula $D = \frac { M } { V }$ and round to the nearest hundredth, if necessary.)

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $\frac { ( 5,000,000 ) ( 78,000 ) } { 39,000,000,000 }$

Solve -

Multiply and leave your answer in exponent form. - $\left( x ^ { 3 } \right) \left( x ^ { 4 } \right)$

Write in decimal notation. - $9.254 \times 10 ^ { - 6 }$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $( - 3 x y ) ^ { 4 }$

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $( 180,000,000 ) ( 0.00003 ) ( 2000 ) ( 0.003 )$

Solve the problem. -The lengths and the widths of the following two rectangles are labeled. Create a polynomial that describes the sum of the area of these two rectangles.

Perform the indicated operations. - $\left( 7 x ^ { 2 } + 13 x + 15 \right) + \left( - 5 x ^ { 2 } + 6 x - 9 \right)$

Solve the problem. - $( x - 8 y ) ( x - 5 y )$

Solve. -Approximately $7 \times 10 ^ { 3 }$ employees of a certain company average $\$ 30,000$ each year in salary. What is the total amount earned by all the employees of this company per year? Write your answer in scientific notation.

Write in simplest exponent form. -x · x · x · x

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Systems of Linear Equations and Inequalities

Factoring

Rational Expressions and Equations

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Additional Properties of Functions

Logarithmic and Exponential Functions

Filters

Exam 5: Exponents and Polynomials

Write in decimal notation. - 1.77×10−41.77 \times 10 ^ { - 4 }1.77×10−4

Solve the problem. - 12x5(−8x6+3x4+11)12 x ^ { 5 } \left( - 8 x ^ { 6 } + 3 x ^ { 4 } + 11 \right)12x5(−8x6+3x4+11)

Multiply and leave your answer in exponent form. - (7x)(8x5)(x7)( 7 x ) \left( 8 x ^ { 5 } \right) \left( x ^ { 7 } \right)(7x)(8x5)(x7)

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - 12m3n104m2n7\frac { 12 m ^ { 3 } n ^ { 10 } } { 4 m ^ { 2 } n ^ { 7 } }4m2n712m3n10​

Solve the problem. - 14x4y6(3x−10y+8)\frac { 1 } { 4 } x ^ { 4 } y ^ { 6 } ( 3 x - 10 y + 8 )41​x4y6(3x−10y+8)

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - (3x2y3z4)3\left( \frac { 3 x ^ { 2 } y ^ { 3 } } { z ^ { 4 } } \right) ^ { 3 }(z43x2y3​)3

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - (xy5x6y)−2\left( \frac { x y ^ { 5 } } { x ^ { 6 } y } \right) ^ { - 2 }(x6yxy5​)−2

Perform the indicated operations. - (3x−8)+(6x−9)( 3 x - 8 ) + ( 6 x - 9 )(3x−8)+(6x−9)

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - (5,000,000)(78,000)39,000,000,000\frac { ( 5,000,000 ) ( 78,000 ) } { 39,000,000,000 }39,000,000,000(5,000,000)(78,000)​