Question 1

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
-$x^{-2}$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $- x ^ { 2 }$ 
C)  $x ^ { 1 / 2 }$ 
D)  $= -\frac { 1 } { x ^ { 2 } }$ 
A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $- x ^ { 2 }$ 
C)  $x ^ { 1 / 2 }$ 
D)  $= -\frac { 1 } { x ^ { 2 } }$

Question 2

Solve the problem.
-$( x - 7 ) ( x + 3 )$

Accepted Answer

A)  $x ^ { 2 } - 5 x - 21$ 
B)  $x ^ { 2 } - 4 x - 5$ 
C)  $x ^ { 2 } - 4 x - 21$ 
D)  $x ^ { 2 } - 21 x - 4$ 
A)  $x ^ { 2 } - 5 x - 21$ 
B)  $x ^ { 2 } - 4 x - 5$ 
C)  $x ^ { 2 } - 4 x - 21$ 
D)  $x ^ { 2 } - 21 x - 4$

Question 3

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
-$$x ^ { - 8 } \cdot x ^ { 2 }$$

Accepted Answer

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

Question 4

Solve.
-The dimensions of the sides of the following figures are labeled. Create a polynomial that describes the sum of the area of these figures.

Accepted Answer

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

Question 5

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
-$2 ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 16 }$ 
C)  16 
D)  $- 16$ 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 16 }$ 
C)  16 
D)  $- 16$

Question 6

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
-$\frac { 3 x ^ { - 2 } y ^ { - 2 } } { 8 z ^ { - 5 } }$

Accepted Answer

A)  $\frac { 3 z ^ { 5 } } { 8 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 8 z ^ { 5 } } { 3 x ^ { 2 } y ^ { 2 } }$ 
C)  $\frac { 3 } { 8 x ^ { 2 } y ^ { 2 } z ^ { 5 } }$ 
D)  $\frac { 32,768 z ^ { 5 } } { 9 x ^ { 2 } y ^ { 2 } }$ 
A)  $\frac { 3 z ^ { 5 } } { 8 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 8 z ^ { 5 } } { 3 x ^ { 2 } y ^ { 2 } }$ 
C)  $\frac { 3 } { 8 x ^ { 2 } y ^ { 2 } z ^ { 5 } }$ 
D)  $\frac { 32,768 z ^ { 5 } } { 9 x ^ { 2 } y ^ { 2 } }$

Question 7

Write in decimal notation.
-$1.686 \times 10 ^ { - 5 }$

Accepted Answer

A)  $0.00001686$ 
B)  $0.0001686$ 
C)  $- 168,600$ 
D)  $0.000001686$ 
A)  $0.00001686$ 
B)  $0.0001686$ 
C)  $- 168,600$ 
D)  $0.000001686$

Question 8

Write in decimal notation.
-$$2.0138 \times 10 ^ { - 7 }$$

Accepted Answer

A)  $0.0000020138$ 
B)  $0.000000020138$ 
C)  $- 201380,000$ 
D)  $0.00000020138$ 
A)  $0.0000020138$ 
B)  $0.000000020138$ 
C)  $- 201380,000$ 
D)  $0.00000020138$

Question 9

Solve the problem.
-$$- 12 a ^ { 3 } b ^ { 7 } \left( - 11 a ^ { 4 } b ^ { 9 } + 4 b ^ { 7 } + 11 a \right)$$

Accepted Answer

A)  $a ^ { 4 } b ^ { 9 } - 48 b ^ { 7 } - 132 a$ 
B)  $\quad a ^ { 7 } b ^ { 16 } - 48 a ^ { 3 } b ^ { 14 } - 132 a ^ { 4 } b ^ { 7 }$ 
C)  $a ^ { 7 } b ^ { 16 } - 48 a ^ { 3 } b ^ { 14 } + 11 a$ 
D)  $\quad a ^ { 7 } b ^ { 16 } + 4 b ^ { 7 } + 11 a$ 
A)  $a ^ { 4 } b ^ { 9 } - 48 b ^ { 7 } - 132 a$ 
B)  $\quad a ^ { 7 } b ^ { 16 } - 48 a ^ { 3 } b ^ { 14 } - 132 a ^ { 4 } b ^ { 7 }$ 
C)  $a ^ { 7 } b ^ { 16 } - 48 a ^ { 3 } b ^ { 14 } + 11 a$ 
D)  $\quad a ^ { 7 } b ^ { 16 } + 4 b ^ { 7 } + 11 a$

Question 10

Solve.
-The dimensions of the sides of the following figure are labeled. Create a polynomial that describes the perimeter of this figure.

Accepted Answer

A)  $2 x ^ { 2 } - 7 x + 1$ 
B)  $x ^ { 2 } - 7 x + 1$ 
C)  $2 x ^ { 2 } + 13 x + 9$ 
D)  $2 x ^ { 2 } - 5 x + 1$ 
A)  $2 x ^ { 2 } - 7 x + 1$ 
B)  $x ^ { 2 } - 7 x + 1$ 
C)  $2 x ^ { 2 } + 13 x + 9$ 
D)  $2 x ^ { 2 } - 5 x + 1$

Question 11

Perform the indicated operations.
-$$\left( 4 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 9 x y + 6 y ^ { 2 } \right)$$

Accepted Answer

A)  $5 x ^ { 2 } + 8 x y + 5 y ^ { 2 }$ 
B)  $5 x ^ { 2 } + 10 x y + 7 y ^ { 2 }$ 
C)  $3 x ^ { 2 } - 10 x y - 7 y ^ { 2 }$ 
D)  $4 x ^ { 2 } + 9 x y + 6 y ^ { 2 }$ 
A)  $5 x ^ { 2 } + 8 x y + 5 y ^ { 2 }$ 
B)  $5 x ^ { 2 } + 10 x y + 7 y ^ { 2 }$ 
C)  $3 x ^ { 2 } - 10 x y - 7 y ^ { 2 }$ 
D)  $4 x ^ { 2 } + 9 x y + 6 y ^ { 2 }$

Question 12

Write in scientific notation.
-0.000007714

Accepted Answer

A)  $7.714 \times 10 ^ { - 7 }$ 
B)  $7.714 \times 10 ^ { 6 }$ 
C)  $7.714 \times 10 ^ { - 5 }$ 
D)  $7.714 \times 10 ^ { - 6 }$ 
A)  $7.714 \times 10 ^ { - 7 }$ 
B)  $7.714 \times 10 ^ { 6 }$ 
C)  $7.714 \times 10 ^ { - 5 }$ 
D)  $7.714 \times 10 ^ { - 6 }$

Question 13

Write in decimal notation.
-$$4.5369 \times 10 ^ { 5 }$$

Accepted Answer

A)  453,690 
B)  $4,536,900$ 
C)  $226.845$ 
D)  45,369 
A)  453,690 
B)  $4,536,900$ 
C)  $226.845$ 
D)  45,369

Question 14

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$\frac { 12,000,000,000 } { 0.00002 }$

Accepted Answer

A)  $6 \times 10 ^ { 14 }$ 
B)  $10 \times 10 ^ { 13 }$ 
C)  $10 \times 10 ^ { 14 }$ 
D)  $6 \times 10 ^ { 13 }$ 
A)  $6 \times 10 ^ { 14 }$ 
B)  $10 \times 10 ^ { 13 }$ 
C)  $10 \times 10 ^ { 14 }$ 
D)  $6 \times 10 ^ { 13 }$

Question 15

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { a ^ { 9 } } { a }$

Accepted Answer

A)  $a ^ { 9 } - a$ 
B)  $a ^ { 8 }$ 
C)  $a 10$ 
D)  9 
A)  $a ^ { 9 } - a$ 
B)  $a ^ { 8 }$ 
C)  $a 10$ 
D)  9

Question 16

Multiply and leave your answer in exponent form.
-$$\left( - 5 x ^ { 4 } \right) \left( - 9 x ^ { 6 } \right)$$

Accepted Answer

A)  $- 45 x 10$ 
B)  $- 45 x ^ { 24 }$ 
C)  $45 x ^ { 10}$ 
D)  $45 x ^ { 24 }$ 
A)  $- 45 x 10$ 
B)  $- 45 x ^ { 24 }$ 
C)  $45 x ^ { 10}$ 
D)  $45 x ^ { 24 }$

Question 17

Write in scientific notation.
-660,000

Accepted Answer

A)  $6.6 \times 10 ^ { - 4 }$ 
B)  $6.6 \times 10 ^ { 5 }$ 
C)  $6.6 \times 10 ^ { 4 }$ 
D)  $6.6 \times 10 ^ { - 5 }$ 
A)  $6.6 \times 10 ^ { - 4 }$ 
B)  $6.6 \times 10 ^ { 5 }$ 
C)  $6.6 \times 10 ^ { 4 }$ 
D)  $6.6 \times 10 ^ { - 5 }$

Question 18

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { 14 x ^ { 7 } y ^ { 5 } z ^ { 6 } } { 98 x ^ { 3 } y ^ { 8 } }$

Accepted Answer

A)  $\frac { 7 x ^ { 4 } z ^ { 6 } } { y ^ { 3 } }$ 
B)  $\frac { 7 x ^ { 4 } } { y ^ { 3 } z ^ { 6 } }$ 
C)  $\frac { x ^ { 4 } } { 7 y ^ { 3 } }$ 
D)  $\frac { x ^ { 4 } z ^ { 6 } } { 7 y ^ { 3 } }$ 
A)  $\frac { 7 x ^ { 4 } z ^ { 6 } } { y ^ { 3 } }$ 
B)  $\frac { 7 x ^ { 4 } } { y ^ { 3 } z ^ { 6 } }$ 
C)  $\frac { x ^ { 4 } } { 7 y ^ { 3 } }$ 
D)  $\frac { x ^ { 4 } z ^ { 6 } } { 7 y ^ { 3 } }$

Question 19

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
-$$\left( x ^ { - 4 } y ^ { 6 } \right) ^ { - 1 }$$

Accepted Answer

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

Question 20

Solve.
-$$20 x ^ { 7 } + 5 x - 4$$

Accepted Answer

A)  trinomial, degree 7 
B)  trinomial, degree 8 
C)  binomial, degree 8 
D)  trinomial, degree 9 
A)  trinomial, degree 7 
B)  trinomial, degree 8 
C)  binomial, degree 8 
D)  trinomial, degree 9

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - $x^{-2}$

Solve the problem. - $( x - 7 ) ( x + 3 )$

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - $x ^ { - 8 } \cdot x ^ { 2 }$

Solve. -The dimensions of the sides of the following figures are labeled. Create a polynomial that describes the sum of the area of these figures.

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - $2 ^ { - 4 }$

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - $\frac { 3 x ^ { - 2 } y ^ { - 2 } } { 8 z ^ { - 5 } }$

Write in decimal notation. - $1.686 \times 10 ^ { - 5 }$

Write in decimal notation. - $2.0138 \times 10 ^ { - 7 }$

Solve the problem. - $- 12 a ^ { 3 } b ^ { 7 } \left( - 11 a ^ { 4 } b ^ { 9 } + 4 b ^ { 7 } + 11 a \right)$

Solve. -The dimensions of the sides of the following figure are labeled. Create a polynomial that describes the perimeter of this figure.

Perform the indicated operations. - $\left( 4 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 9 x y + 6 y ^ { 2 } \right)$

Write in scientific notation. -0.000007714

Write in decimal notation. - $4.5369 \times 10 ^ { 5 }$

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $\frac { 12,000,000,000 } { 0.00002 }$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { a ^ { 9 } } { a }$

Multiply and leave your answer in exponent form. - $\left( - 5 x ^ { 4 } \right) \left( - 9 x ^ { 6 } \right)$

Write in scientific notation. -660,000

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { 14 x ^ { 7 } y ^ { 5 } z ^ { 6 } } { 98 x ^ { 3 } y ^ { 8 } }$

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - $\left( x ^ { - 4 } y ^ { 6 } \right) ^ { - 1 }$

Solve. - $20 x ^ { 7 } + 5 x - 4$

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

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - x−2x^{-2}x−2

Solve the problem. - (x−7)(x+3)( x - 7 ) ( x + 3 )(x−7)(x+3)

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. - x−8⋅x2x ^ { - 8 } \cdot x ^ { 2 }x−8⋅x2