Question 1

For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$$f ( x ) = 5 x ^ { 6 } , g ( x ) = - 4 x ^ { 4 } + 8 x ^ { 2 } - 1$$

Accepted Answer

A)  $- 20 x ^ { 4 } + 40 x ^ { 2 } - 5$ 
B)  $- 20 x ^ { 10 } + 8 x ^ { 2 } - 1$ 
C)  $- 20 x ^ { 10 } + 40 x ^ { 8 }$ 
D)  $- 20 x ^ { 10 } + 40 x ^ { 8 } - 5 x ^ { 6 }$ 
A)  $- 20 x ^ { 4 } + 40 x ^ { 2 } - 5$ 
B)  $- 20 x ^ { 10 } + 8 x ^ { 2 } - 1$ 
C)  $- 20 x ^ { 10 } + 40 x ^ { 8 }$ 
D)  $- 20 x ^ { 10 } + 40 x ^ { 8 } - 5 x ^ { 6 }$

Question 2

Find the missing factor or exponent(s).
-$\left( x ^ { 6 } \right) ^ { ? } \left( x ^ { 6 } \right) ^ { 3 } = x ^ { 42 }$

Accepted Answer

A)  18 
B)  24 
C)  6 
D)  4 
A)  18 
B)  24 
C)  6 
D)  4

Question 3

Perform the indicated calculation. Express your answer using scientific notation.
-$$\left( 9.24 \times 10 ^ { 5 } \right) \div \left( 4.4 \times 10 ^ { - 6 } \right)$$

Accepted Answer

A)  $4.2 \times 10^{11}$ 
B)  $2.1 \times 10 ^ { - 1 }$ 
C)  $2.1 \times 10^{11}$ 
D)  $4.2 \times 10 ^ { - 1 }$ 
A)  $4.2 \times 10^{11}$ 
B)  $2.1 \times 10 ^ { - 1 }$ 
C)  $2.1 \times 10^{11}$ 
D)  $4.2 \times 10 ^ { - 1 }$

Question 4

Find the missing monomial, factor or term.
-$$- 6 x ^ { 5 } \cdot ? = - 54 x ^ { 8 }$$

Accepted Answer

A)  $9 x ^ { 3 }$ 
B)  $15 x ^ { 3 }$ 
C)  $- 9 x ^ { 3 }$ 
D)  $x ^ { 3 }$ 
A)  $9 x ^ { 3 }$ 
B)  $15 x ^ { 3 }$ 
C)  $- 9 x ^ { 3 }$ 
D)  $x ^ { 3 }$

Question 5

Perform the indicated calculation. Express your answer using scientific notation.
-$$\left( 6.6 \times 10 ^ { - 3 } \right) \left( 7.4 \times 10 ^ { 8 } \right)$$

Accepted Answer

A)  $14 \times 10^{11}$ 
B)  $4.884 \times 10 ^ { 5 }$ 
C)  $4.884 \times 10 ^ { 6 }$ 
D)  $1.57 \times 10 ^ { 5 }$ 
A)  $14 \times 10^{11}$ 
B)  $4.884 \times 10 ^ { 5 }$ 
C)  $4.884 \times 10 ^ { 6 }$ 
D)  $1.57 \times 10 ^ { 5 }$

Question 6

-$( 11 x ) ^ { 0 }$

Accepted Answer

A)  $11 \mathrm { x }$ 
B)  11 
C)  0 
D)  1 
A)  $11 \mathrm { x }$ 
B)  11 
C)  0 
D)  1

Question 7

Simplify.
-$\left( 4 ^ { 2 } \right) ^ { 4 }$

Accepted Answer

A)  65,536 
B)  10 
C)  4096 
D)  32 
A)  65,536 
B)  10 
C)  4096 
D)  32

Question 8

Simplify.
-2^ 3* 2

Accepted Answer

A)  16 
B)  32 
C)  4 
D)  8 
A)  16 
B)  32 
C)  4 
D)  8

Question 9

Identify the polynomial as a monomial, binomial or trinomial.
-$$- 18 x - 4$$

Accepted Answer

A)  Binomial 
B)  Trinomial 
C)  Monomial 
A)  Binomial 
B)  Trinomial 
C)  Monomial

Question 10

Identify the polynomial as a monomial, binomial or trinomial.
-$- 16 x ^ { 2 }$

Accepted Answer

A)  Monomial 
B)  Trinomial 
C)  Binomial 
A)  Monomial 
B)  Trinomial 
C)  Binomial

Question 11

Find the missing dividend or divisor.
-$\frac { 10 x ^ { 8 } } { ? } = - 2 x ^ { 6 }$

Accepted Answer

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

Question 12

-$\left( \frac { x } { 4 } \right) ^ { 3 }$

Accepted Answer

A)  $64 x ^ { 3 }$ 
B)  $\frac { x ^ { 3 } } { 4 }$ 
C)  $\frac { x ^ { 3 } } { 64 }$ 
D)  $\frac { x } { 64 }$ 
A)  $64 x ^ { 3 }$ 
B)  $\frac { x ^ { 3 } } { 4 }$ 
C)  $\frac { x ^ { 3 } } { 64 }$ 
D)  $\frac { x } { 64 }$

Question 13

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero
real numbers.)
-$\left( n ^ { 9 } \right) ^ { - 3 }$

Accepted Answer

A)  $\frac { 1 } { n ^ { 27 } }$ 
B)  $n ^ { 6 }$ 
C)  $n ^ { 27 }$ 
D)  $\frac { 1 } { n ^ { 6 } }$ 
A)  $\frac { 1 } { n ^ { 27 } }$ 
B)  $n ^ { 6 }$ 
C)  $n ^ { 27 }$ 
D)  $\frac { 1 } { n ^ { 6 } }$

Question 14

Divide. Assume all variables are nonzero.
-$\frac { 56 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 10 } } { 7 \mathrm { x } ^ { 2 } \mathrm { y } }$

Accepted Answer

A)  $8 x ^ { 4 } y ^ { 10 }$ 
B)  $8 x ^ { 6 } y ^ { 9 }$ 
C)  $49 x ^ { 6 } y ^ { 10 }$ 
D)  $8 x ^ { 6 } y^{ 10}$ 
A)  $8 x ^ { 4 } y ^ { 10 }$ 
B)  $8 x ^ { 6 } y ^ { 9 }$ 
C)  $49 x ^ { 6 } y ^ { 10 }$ 
D)  $8 x ^ { 6 } y^{ 10}$

Question 15

Determine the coefficient and the degree of each term in the polynomial
-$$x ^ { 5 } + 7 x ^ { 3 } - x - 4$$

Accepted Answer

A)  Coefficients: $1,7,0 , - 4$
degrees: $5,3,1,1$ 
B)  Coefficients: $1,7 , - 1 , - 4$ 
degrees: $5,3,1,0$ 
C)  Coefficients: $1,7 , - 1,4$
degrees: $5,4,1,0$ 
D)  Coefficients: $1,7,1,4$  
degrees: $5,3,1,0$ 
A)  Coefficients: $1,7,0 , - 4$
degrees: $5,3,1,1$ 
B)  Coefficients: $1,7 , - 1 , - 4$ 
degrees: $5,3,1,0$ 
C)  Coefficients: $1,7 , - 1,4$
degrees: $5,4,1,0$ 
D)  Coefficients: $1,7,1,4$  
degrees: $5,3,1,0$

Question 16

-$$\left( \frac { 2 a ^ { 2 } b ^ { 4 } } { c ^ { 3 } } \right) ^ { 3 }$$

Accepted Answer

A)  $\frac { 2 a ^ { 6 } b ^ { 12 } } { c ^ { 9 } }$ 
B)  $\frac { 8 a ^ { 5 } b ^ { 7 } } { c ^ { 6 } }$ 
C)  $\frac { 2 a ^ { 6 } b ^ { 12 } } { c ^ { 6 } }$ 
D)  $\frac { 8 a ^ { 6 } b ^ { 12 } } { c ^ { 9 } }$ 
A)  $\frac { 2 a ^ { 6 } b ^ { 12 } } { c ^ { 9 } }$ 
B)  $\frac { 8 a ^ { 5 } b ^ { 7 } } { c ^ { 6 } }$ 
C)  $\frac { 2 a ^ { 6 } b ^ { 12 } } { c ^ { 6 } }$ 
D)  $\frac { 8 a ^ { 6 } b ^ { 12 } } { c ^ { 9 } }$

Question 17

Divide using long division.
-$$\frac { 4 x ^ { 2 } + 31 x - 26 } { x + 9 }$$

Accepted Answer

A)  $4 x - 5 - \frac { 19 } { x + 9 }$ 
B)  $4 x - 5 + \frac { 19 } { x + 9 }$ 
C)  $4 x + 5 + \frac { 19 } { x + 9 }$ 
D)  $4 x - 5$ 
A)  $4 x - 5 - \frac { 19 } { x + 9 }$ 
B)  $4 x - 5 + \frac { 19 } { x + 9 }$ 
C)  $4 x + 5 + \frac { 19 } { x + 9 }$ 
D)  $4 x - 5$

Question 18

Convert the given number to scientific notation.
-1,037,000,000,000,000

Accepted Answer

A)  $ 1.037 \times 10^{15} $ 
B)  $ 1.037 \times 10^{-15} $ 
C)  $ 1037 \times 1012 $ 
D)  $ 1037 \times 10^{-12} $ 
A)  $ 1.037 \times 10^{15} $ 
B)  $ 1.037 \times 10^{-15} $ 
C)  $ 1037 \times 1012 $ 
D)  $ 1037 \times 10^{-12} $

Question 19

Identify the polynomial as a monomial, binomial or trinomial.
-$15 x$

Accepted Answer

A)  Binomial 
B)  Trinomial 
C)  Monomial 
A)  Binomial 
B)  Trinomial 
C)  Monomial

Question 20

Convert the given number to scientific notation.
-0.000014914

Accepted Answer

A)  $1.4914 \times 10 ^ { - 5 }$ 
B)  $1.4914 \times 10 ^ { - 4 }$ 
C)  $1.4914 \times 10 ^ { 5 }$ 
D)  $1.4914 \times 10 ^ { 4 }$ 
A)  $1.4914 \times 10 ^ { - 5 }$ 
B)  $1.4914 \times 10 ^ { - 4 }$ 
C)  $1.4914 \times 10 ^ { 5 }$ 
D)  $1.4914 \times 10 ^ { 4 }$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = 5 x ^ { 6 } , g ( x ) = - 4 x ^ { 4 } + 8 x ^ { 2 } - 1$

Find the missing factor or exponent(s). - $\left( x ^ { 6 } \right) ^ { ? } \left( x ^ { 6 } \right) ^ { 3 } = x ^ { 42 }$

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 9.24 \times 10 ^ { 5 } \right) \div \left( 4.4 \times 10 ^ { - 6 } \right)$

Find the missing monomial, factor or term. - $- 6 x ^ { 5 } \cdot ? = - 54 x ^ { 8 }$

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 6.6 \times 10 ^ { - 3 } \right) \left( 7.4 \times 10 ^ { 8 } \right)$

$- ( 11 x ) ^ { 0 }$ $- ( 11 x ) ^ { 0 }$ - $( 11 x ) ^ { 0 }$

Simplify. - $\left( 4 ^ { 2 } \right) ^ { 4 }$

Simplify. -2^ 3* 2

Identify the polynomial as a monomial, binomial or trinomial. - $- 18 x - 4$

Identify the polynomial as a monomial, binomial or trinomial. - $- 16 x ^ { 2 }$

Find the missing dividend or divisor. - $\frac { 10 x ^ { 8 } } { ? } = - 2 x ^ { 6 }$

$- \left( \frac { x } { 4 } \right) ^ { 3 }$ $- \left( \frac { x } { 4 } \right) ^ { 3 }$ - $\left( \frac { x } { 4 } \right) ^ { 3 }$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left( n ^ { 9 } \right) ^ { - 3 }$

Divide. Assume all variables are nonzero. - $\frac { 56 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 10 } } { 7 \mathrm { x } ^ { 2 } \mathrm { y } }$

Determine the coefficient and the degree of each term in the polynomial - $x ^ { 5 } + 7 x ^ { 3 } - x - 4$

$- \left( \frac { 2 a ^ { 2 } b ^ { 4 } } { c ^ { 3 } } \right) ^ { 3 }$ $- \left( \frac { 2 a ^ { 2 } b ^ { 4 } } { c ^ { 3 } } \right) ^ { 3 }$ - $\left( \frac { 2 a ^ { 2 } b ^ { 4 } } { c ^ { 3 } } \right) ^ { 3 }$

Divide using long division. - $\frac { 4 x ^ { 2 } + 31 x - 26 } { x + 9 }$

Convert the given number to scientific notation. -1,037,000,000,000,000

Identify the polynomial as a monomial, binomial or trinomial. - $15 x$

Convert the given number to scientific notation. -0.000014914

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

For the given functions f(x) and g(x), find f(x) ∙ g(x). - f(x)=5x6,g(x)=−4x4+8x2−1f ( x ) = 5 x ^ { 6 } , g ( x ) = - 4 x ^ { 4 } + 8 x ^ { 2 } - 1f(x)=5x6,g(x)=−4x4+8x2−1

Find the missing factor or exponent(s). - (x6)?(x6)3=x42\left( x ^ { 6 } \right) ^ { ? } \left( x ^ { 6 } \right) ^ { 3 } = x ^ { 42 }(x6)?(x6)3=x42

Perform the indicated calculation. Express your answer using scientific notation. - (9.24×105)÷(4.4×10−6)\left( 9.24 \times 10 ^ { 5 } \right) \div \left( 4.4 \times 10 ^ { - 6 } \right)(9.24×105)÷(4.4×10−6)

Find the missing monomial, factor or term. - −6x5⋅?=−54x8- 6 x ^ { 5 } \cdot ? = - 54 x ^ { 8 }−6x5⋅?=−54x8

Perform the indicated calculation. Express your answer using scientific notation. - (6.6×10−3)(7.4×108)\left( 6.6 \times 10 ^ { - 3 } \right) \left( 7.4 \times 10 ^ { 8 } \right)(6.6×10−3)(7.4×108)

- (11x)0( 11 x ) ^ { 0 }(11x)0

Simplify. - (42)4\left( 4 ^ { 2 } \right) ^ { 4 }(42)4