Question 1

Multiply.
-$( b - 7 ) \left( b ^ { 2 } + 7 b - 4 \right)$

Accepted Answer

A)  $b ^ { 3 } + 14 b ^ { 2 } + 53 b - 28$ 
B)  $b ^ { 3 } - 14 b ^ { 2 } - 53 b + 28$ 
C)  $b ^ { 3 } - 53 b + 28$ 
D)  $b ^ { 3 } + 45 b - 28$ 
A)  $b ^ { 3 } + 14 b ^ { 2 } + 53 b - 28$ 
B)  $b ^ { 3 } - 14 b ^ { 2 } - 53 b + 28$ 
C)  $b ^ { 3 } - 53 b + 28$ 
D)  $b ^ { 3 } + 45 b - 28$

Question 2

Simplify the expression.
-$- 4 y ^ { 0 }$

Accepted Answer

A)  $- 3$ 
B)  1 
C)  0 
D)  $- 4$ 
A)  $- 3$ 
B)  1 
C)  0 
D)  $- 4$

Question 3

Simplify the expression.
-$\frac { \left( x ^ { 2 } \right) ^ { 4 } } { ( 2 x ) ^ { 3 } }$

Accepted Answer

A)  $\frac { x ^ { 5 } } { 2 }$ 
B)  $\frac { x ^ { 3 } } { 8 }$ 
C)  $\frac { x ^ { 11 } } { 8 }$ 
D)  $\frac { x ^ { 5 } } { 8 }$ 
A)  $\frac { x ^ { 5 } } { 2 }$ 
B)  $\frac { x ^ { 3 } } { 8 }$ 
C)  $\frac { x ^ { 11 } } { 8 }$ 
D)  $\frac { x ^ { 5 } } { 8 }$

Question 4

Multiply.
-$( 4 x - 8 ) ( 3 x - 3 )$

Accepted Answer

A)  $7 x ^ { 2 } - 36 x - 36$ 
B)  $12 x ^ { 2 } - 36 x + 24$ 
C)  $12 x ^ { 2 } - 36 x - 36$ 
D)  $7 x ^ { 2 } - 36 x + 24$ 
A)  $7 x ^ { 2 } - 36 x - 36$ 
B)  $12 x ^ { 2 } - 36 x + 24$ 
C)  $12 x ^ { 2 } - 36 x - 36$ 
D)  $7 x ^ { 2 } - 36 x + 24$

Question 5

Write the number in scientific notation.
-$0.000000020305$

Accepted Answer

A)  $2.0305 \times 10 ^ { - 7 }$ 
B)  $2.0305 \times 10 ^ { 8 }$ 
C)  $2.0305 \times 10 ^ { - 9 }$ 
D)  $2.0305 \times 10 ^ { - 8 }$ 
A)  $2.0305 \times 10 ^ { - 7 }$ 
B)  $2.0305 \times 10 ^ { 8 }$ 
C)  $2.0305 \times 10 ^ { - 9 }$ 
D)  $2.0305 \times 10 ^ { - 8 }$

Question 6

Use the quotient rule to simplify the expression.
-$\frac { \mathrm { d } ^ { 9 } } { \mathrm {~d} }$

Accepted Answer

A)  $\mathrm { d } ^ { 8 }$ 
B)  $\mathrm { d } ^ { 10 }$ 
C)  9 
D)  $\mathrm { d } ^ { 9 } - \mathrm { d }$ 
A)  $\mathrm { d } ^ { 8 }$ 
B)  $\mathrm { d } ^ { 10 }$ 
C)  9 
D)  $\mathrm { d } ^ { 9 } - \mathrm { d }$

Question 7

Simplify the expression.
-$\left( \frac { 18 \mathrm { t } ^ { 3 } } { 9 \mathrm {~s} ^ { 4 } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 4 t ^ { 5 } } { s ^ { 6 } }$ 
B)  $\frac { 4 t ^ { 6 } } { s ^ { 4 } }$ 
C)  $\frac { 4 t ^ { 6 } } { s ^ { 8 } }$ 
D)  $\frac { 2 t ^ { 6 } } { s ^ { 8 } }$ 
A)  $\frac { 4 t ^ { 5 } } { s ^ { 6 } }$ 
B)  $\frac { 4 t ^ { 6 } } { s ^ { 4 } }$ 
C)  $\frac { 4 t ^ { 6 } } { s ^ { 8 } }$ 
D)  $\frac { 2 t ^ { 6 } } { s ^ { 8 } }$

Question 8

Evaluate the expression with the given replacement values.
-$\frac { 6 } { 7 x ^ { 2 } } ; x = - 5$

Accepted Answer

A)  $- \frac { 6 } { 175 }$ 
B)  $- \frac { 3 } { 35 }$ 
C)  $\frac { 6 } { 175 }$ 
D)  $\frac { 3 } { 35 }$ 
A)  $- \frac { 6 } { 175 }$ 
B)  $- \frac { 3 } { 35 }$ 
C)  $\frac { 6 } { 175 }$ 
D)  $\frac { 3 } { 35 }$

Question 9

Multiply.
-$- 2 x ( 2 x - 3 )$

Accepted Answer

A)  $2 x ^ { 2 } + 6 x$ 
B)  $- 4 x ^ { 2 } - 3 x$ 
C)  $2 x ^ { 2 }$ 
D)  $- 4 x ^ { 2 } + 6 x$ 
A)  $2 x ^ { 2 } + 6 x$ 
B)  $- 4 x ^ { 2 } - 3 x$ 
C)  $2 x ^ { 2 }$ 
D)  $- 4 x ^ { 2 } + 6 x$

Question 10

Simplify the expression.
-$( - 2 ) ^ { 0 } + ( - 7 ) ^ { 0 }$

Accepted Answer

A)  $- 2$ 
B)  2 
C)  0 
D)  $- 9$ 
A)  $- 2$ 
B)  2 
C)  0 
D)  $- 9$

Question 11

Simplify the expression. Write the result using positive exponents only.
-$\left( \frac { 1 } { 4 } \right) ^ { - 2 }$

Accepted Answer

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

Question 12

Use the product rule to simplify the expression. Write the result using exponents.
-$x ^ { 2 } \cdot x ^ { 8 }$

Accepted Answer

A)  $x ^ { 2 }$ 
B)  $x ^ { 11 }$ 
C)  $x ^ { 10 }$ 
D)  $x ^ { 8 }$ 
A)  $x ^ { 2 }$ 
B)  $x ^ { 11 }$ 
C)  $x ^ { 10 }$ 
D)  $x ^ { 8 }$

Question 13

Find the quotient using long division.
-$\frac { x ^ { 2 } - 36 } { x - 6 }$

Accepted Answer

A)  $x + 6$ 
B)  $x - 36$ 
C)  $x ^ { 2 } - 6$ 
D)  $x + 36$ 
A)  $x + 6$ 
B)  $x - 36$ 
C)  $x ^ { 2 } - 6$ 
D)  $x + 36$

Question 14

Solve.
-Find the area of the top of the table. Express the area as a product, then multiply and simplify.

Accepted Answer

A)  $\left( 49 x ^ { 2 } - 154 x - 121 \right) s q$ in. 
B)  $\left( x ^ { 2 } - 121 \right) s q$ in. 
C)  $\left( 49 x ^ { 2 } + 154 x - 121 \right)$ sq in. 
D)  $\left( 49 x ^ { 2 } - 121 \right) s q$ in. 
A)  $\left( 49 x ^ { 2 } - 154 x - 121 \right) s q$ in. 
B)  $\left( x ^ { 2 } - 121 \right) s q$ in. 
C)  $\left( 49 x ^ { 2 } + 154 x - 121 \right)$ sq in. 
D)  $\left( 49 x ^ { 2 } - 121 \right) s q$ in.

Question 15

Find the perimeter.
-

Accepted Answer

A)  $\left( x ^ { 2 } - 18 x + 4 \right)$ units 
B)  $\left( x ^ { 4 } - 36 x ^ { 2 } + 8 \right)$ units 
C)  $\left( x ^ { 4 } - 18 x ^ { 2 } + 4 \right)$ units 
D)  $\left( 4 x ^ { 2 } - 36 x + 8 \right)$ units 
A)  $\left( x ^ { 2 } - 18 x + 4 \right)$ units 
B)  $\left( x ^ { 4 } - 36 x ^ { 2 } + 8 \right)$ units 
C)  $\left( x ^ { 4 } - 18 x ^ { 2 } + 4 \right)$ units 
D)  $\left( 4 x ^ { 2 } - 36 x + 8 \right)$ units

Question 16

Write the number in standard form.
-$7.74 \times 10 ^ { 5 }$

Accepted Answer

A)  387 
B)  $7,740,000$ 
C)  774,000 
D)  77,400 
A)  387 
B)  $7,740,000$ 
C)  774,000 
D)  77,400

Question 17

Simplify the expression. Write the result using positive exponents only.
-$\frac { x ^ { 3 } \left( x ^ { - 9 } \right) ^ { - 8 } } { \left( x ^ { - 7 } \right) ^ { - 2 } }$

Accepted Answer

A)  $x ^ { 61 }$ 
B)  $\frac { 1 } { x ^ { 83 } }$ 
C)  $x ^ { 23 }$ 
D)  $x ^ { 83 }$ 
A)  $x ^ { 61 }$ 
B)  $\frac { 1 } { x ^ { 83 } }$ 
C)  $x ^ { 23 }$ 
D)  $x ^ { 83 }$

Question 18

Perform the indicated operation.
-$\left( 4 n ^ { 7 } - 3 n ^ { 6 } + 13 \right) - \left( 9 n ^ { 7 } - 10 n ^ { 6 } - 10 \right)$

Accepted Answer

A)  $- 5 n ^ { 7 } + 6 n ^ { 6 } + 3$ 
B)  $- 5 n ^ { 7 } + 7 n ^ { 6 } + 3$ 
C)  $- 5 n ^ { 7 } + 7 n ^ { 6 } + 23$ 
D)  $25 n ^ { 13 }$ 
A)  $- 5 n ^ { 7 } + 6 n ^ { 6 } + 3$ 
B)  $- 5 n ^ { 7 } + 7 n ^ { 6 } + 3$ 
C)  $- 5 n ^ { 7 } + 7 n ^ { 6 } + 23$ 
D)  $25 n ^ { 13 }$

Question 19

Write the number in standard form.
-$1.13 \times 10 ^ { - 4 }$

Accepted Answer

A)  $- 113,000$ 
B)  $0.0000113$ 
C)  $0.000113$ 
D)  $0.00113$ 
A)  $- 113,000$ 
B)  $0.0000113$ 
C)  $0.000113$ 
D)  $0.00113$

Question 20

Multiply.
-$7 z ^ { 2 } \left( 5 z ^ { 2 } + 3 z - 8 \right)$

Accepted Answer

A)  $35 z ^ { 4 } + 21 z ^ { 3 } - 56 z ^ { 2 }$ 
B)  $35 z ^ { 4 } + 21 z - 56$ 
C)  $35 z ^ { 4 } + 21 z ^ { 2 } - 56$ 
D)  $12 z ^ { 4 } + 10 z - 1$ 
A)  $35 z ^ { 4 } + 21 z ^ { 3 } - 56 z ^ { 2 }$ 
B)  $35 z ^ { 4 } + 21 z - 56$ 
C)  $35 z ^ { 4 } + 21 z ^ { 2 } - 56$ 
D)  $12 z ^ { 4 } + 10 z - 1$

Multiply. - $( b - 7 ) \left( b ^ { 2 } + 7 b - 4 \right)$

Simplify the expression. - $- 4 y ^ { 0 }$

Simplify the expression. - $\frac { \left( x ^ { 2 } \right) ^ { 4 } } { ( 2 x ) ^ { 3 } }$

Multiply. - $( 4 x - 8 ) ( 3 x - 3 )$

Write the number in scientific notation. - $0.000000020305$

Use the quotient rule to simplify the expression. - $\frac { \mathrm { d } ^ { 9 } } { \mathrm {~d} }$

Simplify the expression. - $\left( \frac { 18 \mathrm { t } ^ { 3 } } { 9 \mathrm {~s} ^ { 4 } } \right) ^ { 2 }$

Evaluate the expression with the given replacement values. - $\frac { 6 } { 7 x ^ { 2 } } ; x = - 5$

Multiply. - $- 2 x ( 2 x - 3 )$

Simplify the expression. - $( - 2 ) ^ { 0 } + ( - 7 ) ^ { 0 }$

Simplify the expression. Write the result using positive exponents only. - $\left( \frac { 1 } { 4 } \right) ^ { - 2 }$

Use the product rule to simplify the expression. Write the result using exponents. - $x ^ { 2 } \cdot x ^ { 8 }$

Find the quotient using long division. - $\frac { x ^ { 2 } - 36 } { x - 6 }$

Solve. -Find the area of the top of the table. Express the area as a product, then multiply and simplify.

Find the perimeter. -

Write the number in standard form. - $7.74 \times 10 ^ { 5 }$

Simplify the expression. Write the result using positive exponents only. - $\frac { x ^ { 3 } \left( x ^ { - 9 } \right) ^ { - 8 } } { \left( x ^ { - 7 } \right) ^ { - 2 } }$

Perform the indicated operation. - $\left( 4 n ^ { 7 } - 3 n ^ { 6 } + 13 \right) - \left( 9 n ^ { 7 } - 10 n ^ { 6 } - 10 \right)$

Write the number in standard form. - $1.13 \times 10 ^ { - 4 }$

Multiply. - $7 z ^ { 2 } \left( 5 z ^ { 2 } + 3 z - 8 \right)$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Multiply. - (b−7)(b2+7b−4)( b - 7 ) \left( b ^ { 2 } + 7 b - 4 \right)(b−7)(b2+7b−4)

Simplify the expression. - −4y0- 4 y ^ { 0 }−4y0

Simplify the expression. - (x2)4(2x)3\frac { \left( x ^ { 2 } \right) ^ { 4 } } { ( 2 x ) ^ { 3 } }(2x)3(x2)4​

Multiply. - (4x−8)(3x−3)( 4 x - 8 ) ( 3 x - 3 )(4x−8)(3x−3)

Write the number in scientific notation. - 0.0000000203050.0000000203050.000000020305

Use the quotient rule to simplify the expression. - d9 d\frac { \mathrm { d } ^ { 9 } } { \mathrm {~d} } dd9​

Simplify the expression. - (18t39 s4)2\left( \frac { 18 \mathrm { t } ^ { 3 } } { 9 \mathrm {~s} ^ { 4 } } \right) ^ { 2 }(9 s418t3​)2

Evaluate the expression with the given replacement values. - 67x2;x=−5\frac { 6 } { 7 x ^ { 2 } } ; x = - 57x26​;x=−5

Multiply. - −2x(2x−3)- 2 x ( 2 x - 3 )−2x(2x−3)

Simplify the expression. - (−2)0+(−7)0( - 2 ) ^ { 0 } + ( - 7 ) ^ { 0 }(−2)0+(−7)0

Simplify the expression. Write the result using positive exponents only. - (14)−2\left( \frac { 1 } { 4 } \right) ^ { - 2 }(41​)−2

Use the product rule to simplify the expression. Write the result using exponents. - x2⋅x8x ^ { 2 } \cdot x ^ { 8 }x2⋅x8

Find the quotient using long division. - x2−36x−6\frac { x ^ { 2 } - 36 } { x - 6 }x−6x2−36​