Question 1

Simplify the following by combining like terms.
-$2 x ^ { 8 } + 8 x ^ { 8 } - 4 x ^ { 8 }$

Accepted Answer

A)  $6 x ^ { 24 }$ 
B)  $- 64 x ^ { 8 }$ 
C)  $6 x ^ { 8 }$ 
D)  cannot be simplified 
A)  $6 x ^ { 24 }$ 
B)  $- 64 x ^ { 8 }$ 
C)  $6 x ^ { 8 }$ 
D)  cannot be simplified

Question 2

Simplify the expression.
-$\frac { 6 x ^ { 8 } } { x ^ { 5 } }$

Accepted Answer

A)  $6 x ^ { 13 }$ 
B)  $18 x$ 
C)  $216 x ^ { 3 }$ 
D)  $6 x ^ { 3 }$ 
A)  $6 x ^ { 13 }$ 
B)  $18 x$ 
C)  $216 x ^ { 3 }$ 
D)  $6 x ^ { 3 }$

Question 3

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( x ^ { 5 } y ^ { 4 } \right) ^ { 2 }$

Accepted Answer

A)  $x ^ { 10 } y ^ { 8 }$ 
B)  $\mathrm { x } ^ { 10 } \mathrm { y } ^ { 4 }$ 
C)  $x ^ { 7 } y ^ { 6 }$ 
D)  $x ^ { 5 } y ^ { 8 }$ 
A)  $x ^ { 10 } y ^ { 8 }$ 
B)  $\mathrm { x } ^ { 10 } \mathrm { y } ^ { 4 }$ 
C)  $x ^ { 7 } y ^ { 6 }$ 
D)  $x ^ { 5 } y ^ { 8 }$

Question 4

Use synthetic division to divide.
-$\left( x ^ { 3 } - 512 \right) \div ( x - 8 )$

Accepted Answer

A)  $x ^ { 2 } + 64$ 
B)  $x ^ { 2 } + 8 x + 64$ 
C)  $x ^ { 2 } - 8 x + 64$ 
D)  $x ^ { 2 } + 8 x - 64$ 
A)  $x ^ { 2 } + 64$ 
B)  $x ^ { 2 } + 8 x + 64$ 
C)  $x ^ { 2 } - 8 x + 64$ 
D)  $x ^ { 2 } + 8 x - 64$

Question 5

Simplify the exponential expression. Write the result using only positive exponents.
-$\left( \frac { x ^ { 3 } y ^ { 2 } } { x ^ { 4 } y ^ { - 3 } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { y ^ { 10 } } { x ^ { 2 } }$ 
B)  $\frac { y ^ { 7 } } { x ^ { 2 } }$ 
C)  $\frac { y ^ { 25 } } { x }$ 
D)  $\frac { y ^ { 25 } } { x ^ { 2 } }$ 
A)  $\frac { y ^ { 10 } } { x ^ { 2 } }$ 
B)  $\frac { y ^ { 7 } } { x ^ { 2 } }$ 
C)  $\frac { y ^ { 25 } } { x }$ 
D)  $\frac { y ^ { 25 } } { x ^ { 2 } }$

Question 6

Simplify the expression. Write the result using positive exponents only.
-$\frac { 5 ^ { - 7 } x ^ { - 2 } y ^ { 3 } } { 5 ^ { - 4 } x ^ { - 5 } y ^ { 6 } }$

Accepted Answer

A)  $\frac { 125 } { x ^ { 3 } y ^ { 3 } }$ 
B)  $\frac { 3 x ^ { 3 } } { y ^ { 3 } }$ 
C)  $\frac { x ^ { 3 } } { 125 y ^ { 3 } }$ 
D)  $\frac { 1 } { 125 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 3 } }$ 
A)  $\frac { 125 } { x ^ { 3 } y ^ { 3 } }$ 
B)  $\frac { 3 x ^ { 3 } } { y ^ { 3 } }$ 
C)  $\frac { x ^ { 3 } } { 125 y ^ { 3 } }$ 
D)  $\frac { 1 } { 125 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 3 } }$

Question 7

Multiply using the FOIL method.
-$( b + 1 ) ( b + 8 )$

Accepted Answer

A)  $b ^ { 2 } + 9 b + 8$ 
B)  $2 b ^ { 2 } + 8$ 
C)  $2 b + 8$ 
D)  $b ^ { 2 } + 9 b + 9$ 
A)  $b ^ { 2 } + 9 b + 8$ 
B)  $2 b ^ { 2 } + 8$ 
C)  $2 b + 8$ 
D)  $b ^ { 2 } + 9 b + 9$

Question 8

Simplify the expression. Write the result using positive exponents only.
-$\left( z ^ { 6 } x ^ { 6 } \right) ^ { - 3 }$

Accepted Answer

A)  $\frac { 1 } { ( z x ) ^ { 36 } }$ 
B)  $\mathrm { z } ^ { 9 } \mathrm { x } ^ { 9 }$ 
C)  $\frac { 1 } { \mathrm { z } ^ { 18 } \mathrm { x } ^ { 18 } }$ 
D)  $z ^ { 3 } x ^ { 3 }$ 
A)  $\frac { 1 } { ( z x ) ^ { 36 } }$ 
B)  $\mathrm { z } ^ { 9 } \mathrm { x } ^ { 9 }$ 
C)  $\frac { 1 } { \mathrm { z } ^ { 18 } \mathrm { x } ^ { 18 } }$ 
D)  $z ^ { 3 } x ^ { 3 }$

Question 9

Simplify. Write the answer in standard form.
-$\left( 2.1 \times 10 ^ { - 3 } \right) \left( 4 \times 10 ^ { - 2 } \right)$

Accepted Answer

A)  $0.00084$ 
B)  $0.0000084$ 
C)  $0.00000084$ 
D)  $0.000084$ 
A)  $0.00084$ 
B)  $0.0000084$ 
C)  $0.00000084$ 
D)  $0.000084$

Question 10

Solve.
-A pebble is hurled upward from the top of a 384 -foot-tall building with an initial velocity of 80 feet per second. Neglecting air resistance, the height $h ( t )$ in feet of the pebble after $t$ seconds is giv the polynomial function
$h ( t ) = - 16 t ^ { 2 } + 80 t + 384$
a. Find the height of the pebble when $t = 1$.
b. Find the height of the pebble when $t = 3.7$.
c. When will the pebble hit the ground?

Accepted Answer

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

Question 11

Use synthetic division to divide.
-$\left( x ^ { 4 } + 625 \right) \div ( x - 5 )$

Accepted Answer

A)  $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$ 
B)  $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 1250 } { x - 5 }$ 
C)  $x ^ { 3 } - 5 x ^ { 2 } + 25 x - 125 + \frac { 1250 } { x - 5 }$ 
D)  $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 625 } { x - 5 }$ 
A)  $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$ 
B)  $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 1250 } { x - 5 }$ 
C)  $x ^ { 3 } - 5 x ^ { 2 } + 25 x - 125 + \frac { 1250 } { x - 5 }$ 
D)  $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 625 } { x - 5 }$

Question 12

Write the number in scientific notation.
-$0.000000386014$

Accepted Answer

A)  $3.86014 \times 10 ^ { - 6 }$ 
B)  $3.86014 \times 10 ^ { 6 }$ 
C)  $3.86014 \times 10 ^ { - 7 }$ 
D)  $3.86014 \times 10 ^ { 7 }$ 
A)  $3.86014 \times 10 ^ { - 6 }$ 
B)  $3.86014 \times 10 ^ { 6 }$ 
C)  $3.86014 \times 10 ^ { - 7 }$ 
D)  $3.86014 \times 10 ^ { 7 }$

Question 13

Simplify the expression. Write the result using positive exponents only.
-$\frac { \mathrm { y } ^ { - 6 } } { \mathrm { y } ^ { 3 } }$

Accepted Answer

A)  $\mathrm { y } ^ { 9 }$ 
B)  $\frac { 1 } { y ^ { 18 } }$ 
C)  $\frac { 1 } { \mathrm { y } ^ { 9 } }$ 
D)  $\frac { 1 } { y ^ { 3 } }$ 
A)  $\mathrm { y } ^ { 9 }$ 
B)  $\frac { 1 } { y ^ { 18 } }$ 
C)  $\frac { 1 } { \mathrm { y } ^ { 9 } }$ 
D)  $\frac { 1 } { y ^ { 3 } }$

Question 14

Perform the indicated operation.
-$( 14 x - 5 ) - ( - 5 x + 12 )$

Accepted Answer

A)  $2 x ^ { 2 }$ 
B)  $9 x + 7$ 
C)  $19 x - 17$ 
D)  $19 x + 7$ 
A)  $2 x ^ { 2 }$ 
B)  $9 x + 7$ 
C)  $19 x - 17$ 
D)  $19 x + 7$

Question 15

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( \frac { x y } { 3 } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { x y ^ { 2 } } { 9 }$ 
B)  $\frac { x ^ { 2 } y ^ { 2 } } { 9 }$ 
C)  $\frac { x ^ { 2 } y ^ { 2 } } { 3 }$ 
D)  $\frac { x y } { 9 }$ 
A)  $\frac { x y ^ { 2 } } { 9 }$ 
B)  $\frac { x ^ { 2 } y ^ { 2 } } { 9 }$ 
C)  $\frac { x ^ { 2 } y ^ { 2 } } { 3 }$ 
D)  $\frac { x y } { 9 }$

Question 16

Use synthetic division to divide.
-$\left( x ^ { 3 } + 27 \right) \div ( x + 3 )$

Accepted Answer

A)  $x ^ { 2 } + 3 x + 9$ 
B)  $x ^ { 2 } + 9$ 
C)  $x ^ { 2 } - 3 x + 9$ 
D)  $x ^ { 2 } + 3 x - 9$ 
A)  $x ^ { 2 } + 3 x + 9$ 
B)  $x ^ { 2 } + 9$ 
C)  $x ^ { 2 } - 3 x + 9$ 
D)  $x ^ { 2 } + 3 x - 9$

Question 17

Perform the indicated operation.
-$\left( 3 x ^ { 2 } - 10 x + 3 \right) - \left( x ^ { 2 } - 3 x + 2 \right) + \left( 7 x ^ { 2 } + 5 \right)$

Accepted Answer

A)  $- 5 x ^ { 2 } - 13 x + 10$ 
B)  $9 x ^ { 2 } - 7 x + 10$ 
C)  $9 x ^ { 2 } - 7 x + 6$ 
D)  $9 x ^ { 2 } + 7 x + 6$ 
A)  $- 5 x ^ { 2 } - 13 x + 10$ 
B)  $9 x ^ { 2 } - 7 x + 10$ 
C)  $9 x ^ { 2 } - 7 x + 6$ 
D)  $9 x ^ { 2 } + 7 x + 6$

Question 18

Simplify the expression. Write the result using positive exponents only.
-$\frac { \left( 6 x ^ { 3 } \right) ^ { 3 } } { x ^ { 15 } }$

Accepted Answer

A)  $\frac { 216 } { x ^ { 9 } }$ 
B)  $\frac { 6 } { x ^ { 6 } }$ 
C)  $\frac { 216 } { x ^ { 6 } }$ 
D)  $\frac { 216 } { x ^ { 24 } }$ 
A)  $\frac { 216 } { x ^ { 9 } }$ 
B)  $\frac { 6 } { x ^ { 6 } }$ 
C)  $\frac { 216 } { x ^ { 6 } }$ 
D)  $\frac { 216 } { x ^ { 24 } }$

Question 19

Evaluate the expression using exponential rules. Write the result in standard notation.
-$\frac { 35 \times 10 ^ { 8 } } { 7 \times 10 ^ { 7 } }$

Accepted Answer

A)  $- 50$ 
B)  50 
C)  $0.5$ 
D)  $- 0.5$ 
A)  $- 50$ 
B)  50 
C)  $0.5$ 
D)  $- 0.5$

Question 20

Multiply.
-$( x + 9 ) \left( x ^ { 3 } + 3 x - 6 \right)$

Accepted Answer

A)  $x ^ { 4 } + 3 x ^ { 2 } - 6 x + 9$ 
B)  $x ^ { 4 } + 9 x ^ { 3 } + 3 x ^ { 2 } + 33 x + 54$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } + 21 x - 54$ 
D)  $x ^ { 4 } + 9 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 54$ 
A)  $x ^ { 4 } + 3 x ^ { 2 } - 6 x + 9$ 
B)  $x ^ { 4 } + 9 x ^ { 3 } + 3 x ^ { 2 } + 33 x + 54$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } + 21 x - 54$ 
D)  $x ^ { 4 } + 9 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 54$

Simplify the following by combining like terms. - $2 x ^ { 8 } + 8 x ^ { 8 } - 4 x ^ { 8 }$

Simplify the expression. - $\frac { 6 x ^ { 8 } } { x ^ { 5 } }$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( x ^ { 5 } y ^ { 4 } \right) ^ { 2 }$

Use synthetic division to divide. - $\left( x ^ { 3 } - 512 \right) \div ( x - 8 )$

Simplify the exponential expression. Write the result using only positive exponents. - $\left( \frac { x ^ { 3 } y ^ { 2 } } { x ^ { 4 } y ^ { - 3 } } \right) ^ { 2 }$

Simplify the expression. Write the result using positive exponents only. - $\frac { 5 ^ { - 7 } x ^ { - 2 } y ^ { 3 } } { 5 ^ { - 4 } x ^ { - 5 } y ^ { 6 } }$

Multiply using the FOIL method. - $( b + 1 ) ( b + 8 )$

Simplify the expression. Write the result using positive exponents only. - $\left( z ^ { 6 } x ^ { 6 } \right) ^ { - 3 }$

Simplify. Write the answer in standard form. - $\left( 2.1 \times 10 ^ { - 3 } \right) \left( 4 \times 10 ^ { - 2 } \right)$

Use synthetic division to divide. - $\left( x ^ { 4 } + 625 \right) \div ( x - 5 )$

Write the number in scientific notation. - $0.000000386014$

Simplify the expression. Write the result using positive exponents only. - $\frac { \mathrm { y } ^ { - 6 } } { \mathrm { y } ^ { 3 } }$

Perform the indicated operation. - $( 14 x - 5 ) - ( - 5 x + 12 )$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( \frac { x y } { 3 } \right) ^ { 2 }$

Use synthetic division to divide. - $\left( x ^ { 3 } + 27 \right) \div ( x + 3 )$

Perform the indicated operation. - $\left( 3 x ^ { 2 } - 10 x + 3 \right) - \left( x ^ { 2 } - 3 x + 2 \right) + \left( 7 x ^ { 2 } + 5 \right)$

Simplify the expression. Write the result using positive exponents only. - $\frac { \left( 6 x ^ { 3 } \right) ^ { 3 } } { x ^ { 15 } }$

Evaluate the expression using exponential rules. Write the result in standard notation. - $\frac { 35 \times 10 ^ { 8 } } { 7 \times 10 ^ { 7 } }$

Multiply. - $( x + 9 ) \left( x ^ { 3 } + 3 x - 6 \right)$

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

Simplify the following by combining like terms. - 2x8+8x8−4x82 x ^ { 8 } + 8 x ^ { 8 } - 4 x ^ { 8 }2x8+8x8−4x8

Simplify the expression. - 6x8x5\frac { 6 x ^ { 8 } } { x ^ { 5 } }x56x8​

Use the power rule and the power of a product or quotient rule to simplify the expression. - (x5y4)2\left( x ^ { 5 } y ^ { 4 } \right) ^ { 2 }(x5y4)2

Use synthetic division to divide. - (x3−512)÷(x−8)\left( x ^ { 3 } - 512 \right) \div ( x - 8 )(x3−512)÷(x−8)

Simplify the exponential expression. Write the result using only positive exponents. - (x3y2x4y−3)2\left( \frac { x ^ { 3 } y ^ { 2 } } { x ^ { 4 } y ^ { - 3 } } \right) ^ { 2 }(x4y−3x3y2​)2

Simplify the expression. Write the result using positive exponents only. - 5−7x−2y35−4x−5y6\frac { 5 ^ { - 7 } x ^ { - 2 } y ^ { 3 } } { 5 ^ { - 4 } x ^ { - 5 } y ^ { 6 } }5−4x−5y65−7x−2y3​

Multiply using the FOIL method. - (b+1)(b+8)( b + 1 ) ( b + 8 )(b+1)(b+8)

Simplify the expression. Write the result using positive exponents only. - (z6x6)−3\left( z ^ { 6 } x ^ { 6 } \right) ^ { - 3 }(z6x6)−3

Simplify. Write the answer in standard form. - (2.1×10−3)(4×10−2)\left( 2.1 \times 10 ^ { - 3 } \right) \left( 4 \times 10 ^ { - 2 } \right)(2.1×10−3)(4×10−2)

Use synthetic division to divide. - (x4+625)÷(x−5)\left( x ^ { 4 } + 625 \right) \div ( x - 5 )(x4+625)÷(x−5)

Write the number in scientific notation. - 0.0000003860140.0000003860140.000000386014

Simplify the expression. Write the result using positive exponents only. - y−6y3\frac { \mathrm { y } ^ { - 6 } } { \mathrm { y } ^ { 3 } }y3y−6​

Perform the indicated operation. - (14x−5)−(−5x+12)( 14 x - 5 ) - ( - 5 x + 12 )(14x−5)−(−5x+12)

Use the power rule and the power of a product or quotient rule to simplify the expression. - (xy3)2\left( \frac { x y } { 3 } \right) ^ { 2 }(3xy​)2

Use synthetic division to divide. - (x3+27)÷(x+3)\left( x ^ { 3 } + 27 \right) \div ( x + 3 )(x3+27)÷(x+3)

Perform the indicated operation. - (3x2−10x+3)−(x2−3x+2)+(7x2+5)\left( 3 x ^ { 2 } - 10 x + 3 \right) - \left( x ^ { 2 } - 3 x + 2 \right) + \left( 7 x ^ { 2 } + 5 \right)(3x2−10x+3)−(x2−3x+2)+(7x2+5)

Simplify the expression. Write the result using positive exponents only. - (6x3)3x15\frac { \left( 6 x ^ { 3 } \right) ^ { 3 } } { x ^ { 15 } }x15(6x3)3​

Evaluate the expression using exponential rules. Write the result in standard notation. - 35×1087×107\frac { 35 \times 10 ^ { 8 } } { 7 \times 10 ^ { 7 } }7×10735×108​

Multiply. - (x+9)(x3+3x−6)( x + 9 ) \left( x ^ { 3 } + 3 x - 6 \right)(x+9)(x3+3x−6)