Question 1

Perform the indicated calculation. Express your answer using scientific notation.
-$( 0.0000000064 ) ( 160,000,000,000 )$

Accepted Answer

A)  $1.02 \times 10 ^ { 4 }$ 
B)  $1.02 \times 10 ^ { 3 }$ 
C)  $1.02 \times 10 ^ { - 3 }$ 
D)  $1.02 \times 10 ^ { 2 }$ 
A)  $1.02 \times 10 ^ { 4 }$ 
B)  $1.02 \times 10 ^ { 3 }$ 
C)  $1.02 \times 10 ^ { - 3 }$ 
D)  $1.02 \times 10 ^ { 2 }$

Question 2

Divide using long division.
-$$\frac { x ^ { 3 } + 8 } { x + 2 }$$

Accepted Answer

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

Question 3

-$$\left( \frac { a ^ { 2 } b ^ { 5 } } { b ^ { 2 } c ^ { 5 } } \right) ^ { 8 }$$

Accepted Answer

A)  0 
B)  $\frac { a ^ { 16 } b ^ { 24 } } { c ^ { 40 } }$ 
C)  $\frac { a ^ { 16 } } { c ^ { 40 } }$ 
D)  $\frac { a ^ { 10 } b ^ { 24 } } { c ^ { 13 } }$ 
A)  0 
B)  $\frac { a ^ { 16 } b ^ { 24 } } { c ^ { 40 } }$ 
C)  $\frac { a ^ { 16 } } { c ^ { 40 } }$ 
D)  $\frac { a ^ { 10 } b ^ { 24 } } { c ^ { 13 } }$

Question 4

Evaluate the polynomial or polynomial function for the given value of the variable.
-$g ( x ) = - 10 x ^ { 2 } + 4 x + 5 , g ( 2 )$

Accepted Answer

A)  $- 27$ 
B)  $- 37$ 
C)  $- 31$ 
D)  $- 7$ 
A)  $- 27$ 
B)  $- 37$ 
C)  $- 31$ 
D)  $- 7$

Question 5

Convert the given number to scientific notation.
-1,086,000,000,000,000,000

Accepted Answer

A)  $ 1086 \times 10^{15} $ 
B)  $ 1.086 \times 10^{18} $ 
C)  $ 1.086 \times 10^{-18} $ 
D)  $ 1086 \times 10^{-15} $ 
A)  $ 1086 \times 10^{15} $ 
B)  $ 1.086 \times 10^{18} $ 
C)  $ 1.086 \times 10^{-18} $ 
D)  $ 1086 \times 10^{-15} $

Question 6

Multiply.
-$$5 ( x + 9 )$$

Accepted Answer

A)  $5 x + 45$ 
B)  $x + 45$ 
C)  $45 \mathrm { x }$ 
D)  $5 x + 9$ 
A)  $5 x + 45$ 
B)  $x + 45$ 
C)  $45 \mathrm { x }$ 
D)  $5 x + 9$

Question 7

Multiply.
-$4 a ^ { 4 } b ^ { 3 } c \cdot 8 b c ^ { 5 } d ^ { 2 }$

Accepted Answer

A)  $32 a ^ { 4 } b ^ { 3 } c ^ { 5 } d ^ { 2 }$ 
B)  $12 a ^ { 4 } b ^ { 4 } c ^ { 6 } d ^ { 2 }$ 
C)  $32 a ^ { 4 } b ^ { 4 } c ^ { 6 } d ^ { 2 }$ 
D)  $32 a ^ { 4 } b ^ { 2 } c ^ { 4 } d ^ { 2 }$ 
A)  $32 a ^ { 4 } b ^ { 3 } c ^ { 5 } d ^ { 2 }$ 
B)  $12 a ^ { 4 } b ^ { 4 } c ^ { 6 } d ^ { 2 }$ 
C)  $32 a ^ { 4 } b ^ { 4 } c ^ { 6 } d ^ { 2 }$ 
D)  $32 a ^ { 4 } b ^ { 2 } c ^ { 4 } d ^ { 2 }$

Question 8

For the given functions f(x) and g(x), perform the indicated operation.
-$$f ( x ) = \left( 3 x ^ { 6 } + 9 x ^ { 3 } - 2 \right) , g ( x ) = \left( 7 x ^ { 6 } + 5 x ^ { 3 } + 7 \right)$$
Find $f ( x ) + g ( x )$.

Accepted Answer

A)  $10 x ^ { 6 } + 14 x ^ { 3 } + 5$ 
B)  $14 x ^ { 6 } + 5 x ^ { 3 } + 10$ 
C)  $29 \mathrm { x } ^ { 9 }$ 
D)  $5 x ^ { 6 } + 8 x ^ { 3 } + 16$ 
A)  $10 x ^ { 6 } + 14 x ^ { 3 } + 5$ 
B)  $14 x ^ { 6 } + 5 x ^ { 3 } + 10$ 
C)  $29 \mathrm { x } ^ { 9 }$ 
D)  $5 x ^ { 6 } + 8 x ^ { 3 } + 16$

Question 9

-$\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 4 }$

Accepted Answer

A)  $\frac { a ^ { 5 } } { b ^ { 20 } }$ 
B)  $\frac { a ^ { 16 } } { b ^ { 5 } }$ 
C)  $\frac { a ^ { 20 } } { b ^ { 16 } }$ 
D)  $\frac { a ^ { 16 } } { b ^ { 20 } }$ 
A)  $\frac { a ^ { 5 } } { b ^ { 20 } }$ 
B)  $\frac { a ^ { 16 } } { b ^ { 5 } }$ 
C)  $\frac { a ^ { 20 } } { b ^ { 16 } }$ 
D)  $\frac { a ^ { 16 } } { b ^ { 20 } }$

Question 10

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\frac { x ^ { - 8 } } { y ^ { - 4 } }$

Accepted Answer

A)  $\frac { y ^ { 4 } } { x ^ { 8 } }$ 
B)  $x y ^ { - 12 }$ 
C)  $x ^ { 8 } y ^ { 4 }$ 
D)  $\frac { 1 } { x ^ { 8 } y ^ { 4 } }$ 
A)  $\frac { y ^ { 4 } } { x ^ { 8 } }$ 
B)  $x y ^ { - 12 }$ 
C)  $x ^ { 8 } y ^ { 4 }$ 
D)  $\frac { 1 } { x ^ { 8 } y ^ { 4 } }$

Question 11

-$\left( \frac { 2 } { x } \right) ^ { 3 }$

Accepted Answer

A)  $\frac { 8 } { x }$ 
B)  $8 x ^ { 3 }$ 
C)  $\frac { 2 } { x ^ { 3 } }$ 
D)  $\frac { 8 } { x ^ { 3 } }$ 
A)  $\frac { 8 } { x }$ 
B)  $8 x ^ { 3 }$ 
C)  $\frac { 2 } { x ^ { 3 } }$ 
D)  $\frac { 8 } { x ^ { 3 } }$

Question 12

Simplify.
- x9 ∙ x3

Accepted Answer

A)  $x ^ { 27 }$ 
B)  $x ^ { 12 }$ 
C)  $( 2 x ) ^ { 12 }$ 
D)  $( 2 x ) ^ { 27 }$ 
A)  $x ^ { 27 }$ 
B)  $x ^ { 12 }$ 
C)  $( 2 x ) ^ { 12 }$ 
D)  $( 2 x ) ^ { 27 }$

Question 13

Multiply.
-$- 5 x ^ { 5 } y ^ { 3 } \cdot 9 x ^ { 8 } y$

Accepted Answer

A)  $4 x ^ { 13 } y ^ { 4 }$ 
B)  $- 45 x ^ { 13 } y ^ { 4 }$ 
C)  $4 x ^ { 40 } y ^ { 3 }$ 
D)  $- 45 \mathrm { x } ^{13} \mathrm { y }^ 3$ 
A)  $4 x ^ { 13 } y ^ { 4 }$ 
B)  $- 45 x ^ { 13 } y ^ { 4 }$ 
C)  $4 x ^ { 40 } y ^ { 3 }$ 
D)  $- 45 \mathrm { x } ^{13} \mathrm { y }^ 3$

Question 14

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$$- 6 m ^ { - 4 }$$

Accepted Answer

A)  $- \frac { 6 } { m ^ { 4 } }$ 
B)  $\frac { 1 } { 1296 m ^ { 4 } }$ 
C)  $- \frac { 1 } { 1296 m ^ { 4 } }$ 
D)  $\frac { 1296 } { \mathrm {~m} ^ { 4 } }$ 
A)  $- \frac { 6 } { m ^ { 4 } }$ 
B)  $\frac { 1 } { 1296 m ^ { 4 } }$ 
C)  $- \frac { 1 } { 1296 m ^ { 4 } }$ 
D)  $\frac { 1296 } { \mathrm {~m} ^ { 4 } }$

Question 15

Add or subtract.
-$$\left( 8 x ^ { 2 } - 6 x + 20 \right) - \left( 4 x ^ { 2 } + 5 x - 40 \right)$$

Accepted Answer

A)  $4 x ^ { 2 } - 11 x + 60$ 
B)  $4 x ^ { 2 } - - 11 x + 60$ 
C)  $4 x ^ { 2 } - 11 x - 20$ 
D)  $4 x ^ { 2 } + 11 x + 60$ 
A)  $4 x ^ { 2 } - 11 x + 60$ 
B)  $4 x ^ { 2 } - - 11 x + 60$ 
C)  $4 x ^ { 2 } - 11 x - 20$ 
D)  $4 x ^ { 2 } + 11 x + 60$

Question 16

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$5 - 2$

Accepted Answer

A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 1 } { 25 }$ 
C)  25 
D)  $- 25$ 
A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 1 } { 25 }$ 
C)  25 
D)  $- 25$

Question 17

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\frac { 8 a ^ { - 5 } b ^ { - 8 } } { c ^ { - 3 } d ^ { 4 } }$

Accepted Answer

A)  $\frac { c ^ { 3 } } { 8 a ^ { 5 } b ^ { 8 } d ^ { 4 } }$ 
B)  $\frac { 8 c ^ { 3 } } { a ^ { 5 } b ^ { 8 } d ^ { 4 } }$ 
C)  $\frac { 8 c ^ { 3 } d ^ { 4 } } { a ^ { 5 } b ^ { 8 } }$ 
D)  $\frac { 1 } { 8 a ^ { 5 } b ^ { 8 } c ^ { 3 } d ^ { 4 } }$ 
A)  $\frac { c ^ { 3 } } { 8 a ^ { 5 } b ^ { 8 } d ^ { 4 } }$ 
B)  $\frac { 8 c ^ { 3 } } { a ^ { 5 } b ^ { 8 } d ^ { 4 } }$ 
C)  $\frac { 8 c ^ { 3 } d ^ { 4 } } { a ^ { 5 } b ^ { 8 } }$ 
D)  $\frac { 1 } { 8 a ^ { 5 } b ^ { 8 } c ^ { 3 } d ^ { 4 } }$

Question 18

Divide. Assume all variables are nonzero.
-$\frac { 56 x ^ { 7 } + 63 x ^ { 2 } - 56 x } { 7 x }$

Accepted Answer

A)  $8 x ^ { 7 } + 9 x ^ { 2 } - 8 x$ 
B)  $8 x ^ { 6 } + 9 x - 8$ 
C)  $56 x ^ { 6 } + 63 x - 56$ 
D)  $8 x ^ { 7 } + 63 x ^ { 2 } - 56 x$ 
A)  $8 x ^ { 7 } + 9 x ^ { 2 } - 8 x$ 
B)  $8 x ^ { 6 } + 9 x - 8$ 
C)  $56 x ^ { 6 } + 63 x - 56$ 
D)  $8 x ^ { 7 } + 63 x ^ { 2 } - 56 x$

Question 19

Add or subtract.
-$$\left( 7 x ^ { 8 } - 9 x ^ { 4 } + 5 x ^ { 2 } + 8 \right) + \left( 5 x ^ { 7 } + 7 x ^ { 4 } - 6 x \right)$$

Accepted Answer

A)  $12 x ^ { 8 } - 16 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$ 
B)  $7 x ^ { 8 } + 5 x ^ { 7 } + 2 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$ 
C)  $7 x ^ { 8 } + 5 x ^ { 7 } - 2 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$ 
D)  $12 x ^ { 8 } - 2 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$ 
A)  $12 x ^ { 8 } - 16 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$ 
B)  $7 x ^ { 8 } + 5 x ^ { 7 } + 2 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$ 
C)  $7 x ^ { 8 } + 5 x ^ { 7 } - 2 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$ 
D)  $12 x ^ { 8 } - 2 x ^ { 4 } + 5 x ^ { 2 } - 6 x + 8$

Question 20

Multiply.
-$- 9 y \left( - 2 y ^ { 4 } \right)$

Accepted Answer

A)  $9 y - 2 y ^ { 4 }$ 
B)  $18 y ^ { 5 }$ 
C)  $- 18 y ^ { 5 }$ 
D)  $- 11 y ^ { 4 }$ 
A)  $9 y - 2 y ^ { 4 }$ 
B)  $18 y ^ { 5 }$ 
C)  $- 18 y ^ { 5 }$ 
D)  $- 11 y ^ { 4 }$

Perform the indicated calculation. Express your answer using scientific notation. - $( 0.0000000064 ) ( 160,000,000,000 )$

Divide using long division. - $\frac { x ^ { 3 } + 8 } { x + 2 }$

$- \left( \frac { a ^ { 2 } b ^ { 5 } } { b ^ { 2 } c ^ { 5 } } \right) ^ { 8 }$ $- \left( \frac { a ^ { 2 } b ^ { 5 } } { b ^ { 2 } c ^ { 5 } } \right) ^ { 8 }$ - $\left( \frac { a ^ { 2 } b ^ { 5 } } { b ^ { 2 } c ^ { 5 } } \right) ^ { 8 }$

Evaluate the polynomial or polynomial function for the given value of the variable. - $g ( x ) = - 10 x ^ { 2 } + 4 x + 5 , g ( 2 )$

Convert the given number to scientific notation. -1,086,000,000,000,000,000

Multiply. - $5 ( x + 9 )$

Multiply. - $4 a ^ { 4 } b ^ { 3 } c \cdot 8 b c ^ { 5 } d ^ { 2 }$

For the given functions f(x) and g(x), perform the indicated operation. - $f ( x ) = \left( 3 x ^ { 6 } + 9 x ^ { 3 } - 2 \right) , g ( x ) = \left( 7 x ^ { 6 } + 5 x ^ { 3 } + 7 \right)$ Find $f ( x ) + g ( x )$ .

$- \left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 4 }$ $- \left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 4 }$ - $\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 4 }$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { x ^ { - 8 } } { y ^ { - 4 } }$

$- \left( \frac { 2 } { x } \right) ^ { 3 }$ $- \left( \frac { 2 } { x } \right) ^ { 3 }$ - $\left( \frac { 2 } { x } \right) ^ { 3 }$

Simplify. - x⁹ ∙ x³

Multiply. - $- 5 x ^ { 5 } y ^ { 3 } \cdot 9 x ^ { 8 } y$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $- 6 m ^ { - 4 }$

Add or subtract. - $\left( 8 x ^ { 2 } - 6 x + 20 \right) - \left( 4 x ^ { 2 } + 5 x - 40 \right)$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $5 - 2$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { 8 a ^ { - 5 } b ^ { - 8 } } { c ^ { - 3 } d ^ { 4 } }$

Divide. Assume all variables are nonzero. - $\frac { 56 x ^ { 7 } + 63 x ^ { 2 } - 56 x } { 7 x }$

Add or subtract. - $\left( 7 x ^ { 8 } - 9 x ^ { 4 } + 5 x ^ { 2 } + 8 \right) + \left( 5 x ^ { 7 } + 7 x ^ { 4 } - 6 x \right)$

Multiply. - $- 9 y \left( - 2 y ^ { 4 } \right)$

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

Perform the indicated calculation. Express your answer using scientific notation. - (0.0000000064)(160,000,000,000)( 0.0000000064 ) ( 160,000,000,000 )(0.0000000064)(160,000,000,000)

Divide using long division. - x3+8x+2\frac { x ^ { 3 } + 8 } { x + 2 }x+2x3+8​

- (a2b5b2c5)8\left( \frac { a ^ { 2 } b ^ { 5 } } { b ^ { 2 } c ^ { 5 } } \right) ^ { 8 }(b2c5a2b5​)8

Evaluate the polynomial or polynomial function for the given value of the variable. - g(x)=−10x2+4x+5,g(2)g ( x ) = - 10 x ^ { 2 } + 4 x + 5 , g ( 2 )g(x)=−10x2+4x+5,g(2)

Convert the given number to scientific notation. -1,086,000,000,000,000,000

Multiply. - 5(x+9)5 ( x + 9 )5(x+9)

Multiply. - 4a4b3c⋅8bc5d24 a ^ { 4 } b ^ { 3 } c \cdot 8 b c ^ { 5 } d ^ { 2 }4a4b3c⋅8bc5d2

For the given functions f(x) and g(x), perform the indicated operation. - f(x)=(3x6+9x3−2),g(x)=(7x6+5x3+7)f ( x ) = \left( 3 x ^ { 6 } + 9 x ^ { 3 } - 2 \right) , g ( x ) = \left( 7 x ^ { 6 } + 5 x ^ { 3 } + 7 \right)f(x)=(3x6+9x3−2),g(x)=(7x6+5x3+7) Find f(x)+g(x)f ( x ) + g ( x )f(x)+g(x) .

- (a4b5)4\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 4 }(b5a4​)4

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - x−8y−4\frac { x ^ { - 8 } } { y ^ { - 4 } }y−4x−8​

- (2x)3\left( \frac { 2 } { x } \right) ^ { 3 }(x2​)3

Simplify. - x9 ∙ x3

Multiply. - −5x5y3⋅9x8y- 5 x ^ { 5 } y ^ { 3 } \cdot 9 x ^ { 8 } y−5x5y3⋅9x8y

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - −6m−4- 6 m ^ { - 4 }−6m−4

Add or subtract. - (8x2−6x+20)−(4x2+5x−40)\left( 8 x ^ { 2 } - 6 x + 20 \right) - \left( 4 x ^ { 2 } + 5 x - 40 \right)(8x2−6x+20)−(4x2+5x−40)

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - 5−25 - 25−2

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - 8a−5b−8c−3d4\frac { 8 a ^ { - 5 } b ^ { - 8 } } { c ^ { - 3 } d ^ { 4 } }c−3d48a−5b−8​

Divide. Assume all variables are nonzero. - 56x7+63x2−56x7x\frac { 56 x ^ { 7 } + 63 x ^ { 2 } - 56 x } { 7 x }7x56x7+63x2−56x​

Add or subtract. - (7x8−9x4+5x2+8)+(5x7+7x4−6x)\left( 7 x ^ { 8 } - 9 x ^ { 4 } + 5 x ^ { 2 } + 8 \right) + \left( 5 x ^ { 7 } + 7 x ^ { 4 } - 6 x \right)(7x8−9x4+5x2+8)+(5x7+7x4−6x)

Multiply. - −9y(−2y4)- 9 y \left( - 2 y ^ { 4 } \right)−9y(−2y4)