Question 1

In simplifying $( x + 4 ) ( x - 2 )$ , the product will have a constant term of $- 8$ .

Accepted Answer

A) True 
 B)False

Question 2

Simplify the following algebraic expression and express your answer using positive exponents only. $a ^ { 10 } a ^ { - 7 }$

Accepted Answer

The answer of Simplify the following algebraic expression and express...

Question 3

Perform the division of the polynomials by monomials. $\frac { - 72 p ^ { 8 } + 81 p ^ { 10 } } { 9 p ^ { 4 } }$

Accepted Answer

The answer of Perform the division of the polynomials by...

Question 4

Any base, except 0, raised to a 0 exponent is equal to 1.

Accepted Answer

A) True 
 B)False

Question 5

Divide the monomials. $\frac { 3 p ^ { 8 } } { p ^ { 3 } }$

Accepted Answer

A)  $24 p ^ { 5 }$ 
B)  $3 p ^ { 5 }$ 
C)  $3 p ^ { 11 }$ 
A)  $24 p ^ { 5 }$ 
B)  $3 p ^ { 5 }$ 
C)  $3 p ^ { 11 }$

Question 6

Remove the parentheses by multiplying and then simplify by combining similar terms. $8 x \left( x ^ { 2 } - 2 x - 8 \right) + x \left( 3 x ^ { 2 } + 8 x - 7 \right)$

Accepted Answer

A)  $11 x ^ { 3 } - 8 x ^ { 2 } - 73 x$ 
B)  $12 x ^ { 3 } - 8 x ^ { 2 } - 71 x$ 
C)  $11 x ^ { 3 } - 10 x ^ { 2 } - 72 x$ 
D)  $12 x ^ { 3 } - 10 x ^ { 2 } - 71 x$ 
E)  $11 x ^ { 3 } - 8 x ^ { 2 } - 71 x$ 
A)  $11 x ^ { 3 } - 8 x ^ { 2 } - 73 x$ 
B)  $12 x ^ { 3 } - 8 x ^ { 2 } - 71 x$ 
C)  $11 x ^ { 3 } - 10 x ^ { 2 } - 72 x$ 
D)  $12 x ^ { 3 } - 10 x ^ { 2 } - 71 x$ 
E)  $11 x ^ { 3 } - 8 x ^ { 2 } - 71 x$

Question 7

Perform the indicated operations. $10 p - [ 10 p - ( 6 p - 9 ) ]$

Accepted Answer

A)  $6 p - 10$ 
B)  $- 6 p - 9$ 
C)  $6 p - 9$ 
D)  $7 p - 9$ 
E)  $6 p + 9$ 
A)  $6 p - 10$ 
B)  $- 6 p - 9$ 
C)  $6 p - 9$ 
D)  $7 p - 9$ 
E)  $6 p + 9$

Question 8

Divide the monomials. $\frac { 18 p ^ { 10 } } { 9 p ^ { 2 } }$

Accepted Answer

A)  $9 p ^ { 12 }$ 
B)  $18 p ^ { 8 }$ 
C)  $2 p ^ { 8 }$ 
D)  $9 p ^ { 9 }$ 
E)  $2 p ^ { 10 }$ 
A)  $9 p ^ { 12 }$ 
B)  $18 p ^ { 8 }$ 
C)  $2 p ^ { 8 }$ 
D)  $9 p ^ { 9 }$ 
E)  $2 p ^ { 10 }$

Question 9

Divide the monomials. $\frac { - 77 p ^ { 4 } w ^ { 12 } } { 7 w ^ { 9 } }$

Accepted Answer

A)  $- 11 p ^ { 4 } w ^ { 3 }$ 
B)  $- 11 p ^ { 3 } w ^ { 4 }$ 
C)  $- 11 w ^ { 3 }$ 
D)  $- 11 p ^ { 4 } w ^ { 5 }$ 
A)  $- 11 p ^ { 4 } w ^ { 3 }$ 
B)  $- 11 p ^ { 3 } w ^ { 4 }$ 
C)  $- 11 w ^ { 3 }$ 
D)  $- 11 p ^ { 4 } w ^ { 5 }$

Question 10

Divide the polynomial by the monomial. $\frac { 30 x ^ { 6 } + 70 x ^ { 12 } + 50 x ^ { 10 } } { 10 x ^ { 4 } }$

Accepted Answer

A)  $20 x ^ { 2 } + 60 x ^ { 8 } + 40 x ^ { 6 }$ 
B)  $20 x ^ { 2 } + 60 x ^ { 11 } + 40 x ^ { 6 }$ 
C)  $3 x ^ { 2 } + 7 x ^ { 8 } + 5 x ^ { 6 }$ 
D)  $3 x ^ { 2 } + 7 x ^ { 11 } + 5 x ^ { 6 }$ 
E)  $3 x ^ { 4 } + 7 x ^ { 8 } + 5 x ^ { 7 }$ 
A)  $20 x ^ { 2 } + 60 x ^ { 8 } + 40 x ^ { 6 }$ 
B)  $20 x ^ { 2 } + 60 x ^ { 11 } + 40 x ^ { 6 }$ 
C)  $3 x ^ { 2 } + 7 x ^ { 8 } + 5 x ^ { 6 }$ 
D)  $3 x ^ { 2 } + 7 x ^ { 11 } + 5 x ^ { 6 }$ 
E)  $3 x ^ { 4 } + 7 x ^ { 8 } + 5 x ^ { 7 }$

Question 11

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }$

Accepted Answer

A)  $\frac { 1 } { 243 x ^ { 11 } y ^ { 35 } }$ 
B)  $\frac { 8 } { x ^ { 30 } y ^ { 12 } }$ 
C)  $\frac { 243 } { x ^ { 11 } y ^ { 12 } }$ 
D)  $\frac { 3 } { 243 x ^ { 30 } y ^ { 35 } }$ 
E)  $\frac { 1 } { 243 x ^ { 30 } y ^ { 35 } }$ 
A)  $\frac { 1 } { 243 x ^ { 11 } y ^ { 35 } }$ 
B)  $\frac { 8 } { x ^ { 30 } y ^ { 12 } }$ 
C)  $\frac { 243 } { x ^ { 11 } y ^ { 12 } }$ 
D)  $\frac { 3 } { 243 x ^ { 30 } y ^ { 35 } }$ 
E)  $\frac { 1 } { 243 x ^ { 30 } y ^ { 35 } }$

Question 12

Determine the degree of the polynomial. $2 y ^ { 5 } n ^ { 4 } + 7 y ^ { 5 } n$

Accepted Answer

A)  4 
B)  21 
C)  5 
D)  9 
E)  20 
A)  4 
B)  21 
C)  5 
D)  9 
E)  20

Question 13

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 10, b = 4 and c = 6.

Accepted Answer

A)  $22 x + 20$ 
B)  $44 x + 40$ 
C)  $22 x - 20$ 
D)  $440 x$ 
A)  $22 x + 20$ 
B)  $44 x + 40$ 
C)  $22 x - 20$ 
D)  $440 x$

Question 14

Write the following number in standard decimal form. $( 9.92 ) \left( 10 ^ { 3 } \right)$

Accepted Answer

A)  $9,920$ 
B)  $992,000$ 
C)  $99$ 
D)  $992$ 
E)  $99,200$ 
A)  $9,920$ 
B)  $992,000$ 
C)  $99$ 
D)  $992$ 
E)  $99,200$

Question 15

Multiply. $\left( 5 x ^ { 5 } \right) ( 9 x ) \left( 6 x ^ { 3 } \right)$

Accepted Answer

A)  $273 x ^ { 9 }$ 
B)  $270 x ^ { 9 }$ 
C)  $275 x ^ { 8 }$ 
D)  $270 x ^ { 8 }$ 
E)  $265 x ^ { 8 }$ 
A)  $273 x ^ { 9 }$ 
B)  $270 x ^ { 9 }$ 
C)  $275 x ^ { 8 }$ 
D)  $270 x ^ { 8 }$ 
E)  $265 x ^ { 8 }$

Question 16

Perform the indicated operations and simplify. $( 2 x ) ^ { 3 } \left( 2 x ^ { 3 } \right)$ Enter your answer as $k x ^ { p }$ where k , p are numbers and x is a variable.

Accepted Answer

The answer of Perform the indicated operations and simplify. \((...

Question 17

Evaluate the numerical expression. $\frac { 1 } { 6 ^ { - 3 } }$

Accepted Answer

A)  216 
B)  $\frac { 1 } { 216 }$ 
C)  $- \frac { 1 } { 216 }$ 
D)  729 
A)  216 
B)  $\frac { 1 } { 216 }$ 
C)  $- \frac { 1 } { 216 }$ 
D)  729

Question 18

Simplify the following algebraic expression and express your answer using positive exponents only. $b ^ { 8 } b ^ { - 6 }$

Accepted Answer

A)  $b ^ { 2 }$ 
B)  $\frac { 1 } { b ^ { 2 } }$ 
C)  $\frac { 1 } { b ^ { 14 } }$ 
D)  $- b ^ { 2 }$ 
E)  $b ^ { 14 }$ 
A)  $b ^ { 2 }$ 
B)  $\frac { 1 } { b ^ { 2 } }$ 
C)  $\frac { 1 } { b ^ { 14 } }$ 
D)  $- b ^ { 2 }$ 
E)  $b ^ { 14 }$

Question 19

Express in simplified form the total surface area of the rectangular solid given below, where a = 7 and b = 2.

Accepted Answer

The answer of Express in simplified form the total surface...

Question 20

Remove the parentheses by multiplying and then simplify by combining similar terms. $- 2 ( 9 x + 2 ) - 4 [ 3 x - ( 8 x + 6 ) ]$

Accepted Answer

A)  7 x + 20 
B)  7 x - 28 
C)  2 x - 28 
D)  2 x + 20 
A)  7 x + 20 
B)  7 x - 28 
C)  2 x - 28 
D)  2 x + 20

In simplifying $( x + 4 ) ( x - 2 )$ , the product will have a constant term of $- 8$ .

Simplify the following algebraic expression and express your answer using positive exponents only. $a ^ { 10 } a ^ { - 7 }$

Perform the division of the polynomials by monomials. $\frac { - 72 p ^ { 8 } + 81 p ^ { 10 } } { 9 p ^ { 4 } }$

Any base, except 0, raised to a 0 exponent is equal to 1.

Divide the monomials. $\frac { 3 p ^ { 8 } } { p ^ { 3 } }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $8 x \left( x ^ { 2 } - 2 x - 8 \right) + x \left( 3 x ^ { 2 } + 8 x - 7 \right)$

Perform the indicated operations. $10 p - [ 10 p - ( 6 p - 9 ) ]$

Divide the monomials. $\frac { 18 p ^ { 10 } } { 9 p ^ { 2 } }$

Divide the monomials. $\frac { - 77 p ^ { 4 } w ^ { 12 } } { 7 w ^ { 9 } }$

Divide the polynomial by the monomial. $\frac { 30 x ^ { 6 } + 70 x ^ { 12 } + 50 x ^ { 10 } } { 10 x ^ { 4 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }$

Determine the degree of the polynomial. $2 y ^ { 5 } n ^ { 4 } + 7 y ^ { 5 } n$

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 10, b = 4 and c = 6.

Write the following number in standard decimal form. $( 9.92 ) \left( 10 ^ { 3 } \right)$

Multiply. $\left( 5 x ^ { 5 } \right) ( 9 x ) \left( 6 x ^ { 3 } \right)$

Perform the indicated operations and simplify. $( 2 x ) ^ { 3 } \left( 2 x ^ { 3 } \right)$ Enter your answer as $k x ^ { p }$ where k , p are numbers and x is a variable.

Evaluate the numerical expression. $\frac { 1 } { 6 ^ { - 3 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $b ^ { 8 } b ^ { - 6 }$

Express in simplified form the total surface area of the rectangular solid given below, where a = 7 and b = 2.

Remove the parentheses by multiplying and then simplify by combining similar terms. $- 2 ( 9 x + 2 ) - 4 [ 3 x - ( 8 x + 6 ) ]$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 6: Exponents and Polynomials

In simplifying (x+4)(x−2)( x + 4 ) ( x - 2 )(x+4)(x−2) , the product will have a constant term of −8- 8−8 .

Simplify the following algebraic expression and express your answer using positive exponents only. a10a−7a ^ { 10 } a ^ { - 7 }a10a−7

Perform the division of the polynomials by monomials. −72p8+81p109p4\frac { - 72 p ^ { 8 } + 81 p ^ { 10 } } { 9 p ^ { 4 } }9p4−72p8+81p10​

Any base, except 0, raised to a 0 exponent is equal to 1.

Divide the monomials. 3p8p3\frac { 3 p ^ { 8 } } { p ^ { 3 } }p33p8​

Remove the parentheses by multiplying and then simplify by combining similar terms. 8x(x2−2x−8)+x(3x2+8x−7)8 x \left( x ^ { 2 } - 2 x - 8 \right) + x \left( 3 x ^ { 2 } + 8 x - 7 \right)8x(x2−2x−8)+x(3x2+8x−7)

Perform the indicated operations. 10p−[10p−(6p−9)]10 p - [ 10 p - ( 6 p - 9 ) ]10p−[10p−(6p−9)]

Divide the monomials. 18p109p2\frac { 18 p ^ { 10 } } { 9 p ^ { 2 } }9p218p10​

Divide the monomials. −77p4w127w9\frac { - 77 p ^ { 4 } w ^ { 12 } } { 7 w ^ { 9 } }7w9−77p4w12​

Divide the polynomial by the monomial. 30x6+70x12+50x1010x4\frac { 30 x ^ { 6 } + 70 x ^ { 12 } + 50 x ^ { 10 } } { 10 x ^ { 4 } }10x430x6+70x12+50x10​

Simplify the following algebraic expression and express your answer using positive exponents only. (3x6y7)−5\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }(3x6y7)−5

Determine the degree of the polynomial. 2y5n4+7y5n2 y ^ { 5 } n ^ { 4 } + 7 y ^ { 5 } n2y5n4+7y5n

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 10, b = 4 and c = 6.

Write the following number in standard decimal form. (9.92)(103)( 9.92 ) \left( 10 ^ { 3 } \right)(9.92)(103)

Multiply. (5x5)(9x)(6x3)\left( 5 x ^ { 5 } \right) ( 9 x ) \left( 6 x ^ { 3 } \right)(5x5)(9x)(6x3)

Perform the indicated operations and simplify. (2x)3(2x3)( 2 x ) ^ { 3 } \left( 2 x ^ { 3 } \right)(2x)3(2x3) Enter your answer as kxpk x ^ { p }kxp where k , p are numbers and x is a variable.

Evaluate the numerical expression. 16−3\frac { 1 } { 6 ^ { - 3 } }6−31​

Simplify the following algebraic expression and express your answer using positive exponents only. b8b−6b ^ { 8 } b ^ { - 6 }b8b−6

Express in simplified form the total surface area of the rectangular solid given below, where a = 7 and b = 2.

Remove the parentheses by multiplying and then simplify by combining similar terms. −2(9x+2)−4[3x−(8x+6)]- 2 ( 9 x + 2 ) - 4 [ 3 x - ( 8 x + 6 ) ]−2(9x+2)−4[3x−(8x+6)]

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

In simplifying $( x + 4 ) ( x - 2 )$ , the product will have a constant term of $- 8$ .

Simplify the following algebraic expression and express your answer using positive exponents only. $a ^ { 10 } a ^ { - 7 }$

Perform the division of the polynomials by monomials. $\frac { - 72 p ^ { 8 } + 81 p ^ { 10 } } { 9 p ^ { 4 } }$

Divide the monomials. $\frac { 3 p ^ { 8 } } { p ^ { 3 } }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $8 x \left( x ^ { 2 } - 2 x - 8 \right) + x \left( 3 x ^ { 2 } + 8 x - 7 \right)$

Perform the indicated operations. $10 p - [ 10 p - ( 6 p - 9 ) ]$

Divide the monomials. $\frac { 18 p ^ { 10 } } { 9 p ^ { 2 } }$

Divide the monomials. $\frac { - 77 p ^ { 4 } w ^ { 12 } } { 7 w ^ { 9 } }$

Divide the polynomial by the monomial. $\frac { 30 x ^ { 6 } + 70 x ^ { 12 } + 50 x ^ { 10 } } { 10 x ^ { 4 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }$

Determine the degree of the polynomial. $2 y ^ { 5 } n ^ { 4 } + 7 y ^ { 5 } n$

Write the following number in standard decimal form. $( 9.92 ) \left( 10 ^ { 3 } \right)$

Multiply. $\left( 5 x ^ { 5 } \right) ( 9 x ) \left( 6 x ^ { 3 } \right)$

Perform the indicated operations and simplify. $( 2 x ) ^ { 3 } \left( 2 x ^ { 3 } \right)$ Enter your answer as $k x ^ { p }$ where k , p are numbers and x is a variable.

Evaluate the numerical expression. $\frac { 1 } { 6 ^ { - 3 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $b ^ { 8 } b ^ { - 6 }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $- 2 ( 9 x + 2 ) - 4 [ 3 x - ( 8 x + 6 ) ]$