Exam 1: A Review of Basic Algebra

Perform the division and write the answer without using negative exponents. $\frac { 400 x ^ { 5 } y ^ { 7 } - 240 x ^ { 2 } y ^ { 5 } + 80 x y } { 16 x ^ { 5 } y ^ { 4 } }$

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

A

Simplify the fraction. $\frac { x y + 6 x + 8 y + 48 } { x ^ { 3 } + 512 }$ Assume that denominator is not 0 .

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

D

Simplify each complex fraction. $\frac { x + 1 - \frac { 6 } { x } } { x + 5 + \frac { 6 } { x } }$ Assume that no denominators are 0 .

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

B

How many natural numbers are there between -6.5 and 12.5 on the number line?

(Multiple Choice)

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Question 4

Multiply the expression as you would multiply polynomials. $\left( x ^ { 7 / 2 } + y ^ { 9 / 2 } \right) ^ { 2 }$

(Multiple Choice)

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Question 5

Perform the division.

(Multiple Choice)

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Question 6

Simplify the expression. $\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 3 } r ^ { - 3 } } \right) ^ { 2 }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

(Multiple Choice)

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Question 7

Perform the operation and simplify. $( a - 14 ) ^ { 2 }$

(Multiple Choice)

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Question 8

Simplify the expression. $\frac { \left( 8 ^ { - 2 } z ^ { - 4 } y \right) ^ { - 1 } } { \left( 5 y ^ { 3 } z ^ { - 3 } \right) ^ { 4 } \left( 5 y z ^ { - 3 } \right) ^ { - 1 } }$ Write the answer without using negative exponents.Assume that all variables are restricted to those numbers for which the expression is defined.

(Multiple Choice)

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Question 9

Identify the correct union of intervals for the inequality. $x \leq - 16$ or $x > 5$

(Multiple Choice)

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Question 10

Factor the expression completely. $30 x ^ { 2 } - 13 x y - 56 y ^ { 2 }$

(Multiple Choice)

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Question 11

Factor the expression completely. $4 z ^ { 2 } + 28 z + 49$

(Multiple Choice)

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Question 12

Multiply the expression as you would multiply polynomials. $\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } \right) ^ { 2 }$

(Multiple Choice)

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Question 13

Factor the expression completely. $9 z ^ { 2 } + 42 z + 49$

(Multiple Choice)

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Question 14

Perform the multiplication and simplify. $( x - y ) ( 3 x + 14 y ) ^ { 2 }$

(Multiple Choice)

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Question 15

Rationalize the numerator and simplify. $\frac { \sqrt { 5 } } { 25 }$

(Multiple Choice)

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Question 16

Simplify the fraction. $\frac { 3 x - 9 } { x ^ { 2 } - 9 }$ Assume that the denominator is not 0 .

(Multiple Choice)

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Question 17

Perform the operations and simplify. $\left( 8 x ^ { 3 } - 3 x ^ { 2 } \right) + \left( 5 x ^ { 3 } - 3 x \right)$

(Multiple Choice)

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Question 18

Factor the expression completely. $56 x ^ { 2 } - 29 x y - 40 y ^ { 2 }$

(Multiple Choice)

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Question 19

Perform the division and write the answer without using negative exponents. $\frac { 100 x ^ { 5 } y ^ { 7 } - 60 x ^ { 2 } y ^ { 5 } + 20 x y } { 10 x ^ { 5 } y ^ { 4 } }$

(Multiple Choice)

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Question 20

Perform the division and write the answer without using negative exponents. $\frac { 400 x ^ { 5 } y ^ { 7 } - 240 x ^ { 2 } y ^ { 5 } + 80 x y } { 16 x ^ { 5 } y ^ { 4 } }$

Simplify the fraction. $\frac { x y + 6 x + 8 y + 48 } { x ^ { 3 } + 512 }$ Assume that denominator is not 0 .

Simplify each complex fraction. $\frac { x + 1 - \frac { 6 } { x } } { x + 5 + \frac { 6 } { x } }$ Assume that no denominators are 0 .

How many natural numbers are there between -6.5 and 12.5 on the number line?

Multiply the expression as you would multiply polynomials. $\left( x ^ { 7 / 2 } + y ^ { 9 / 2 } \right) ^ { 2 }$

Perform the division.

Simplify the expression. $\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 3 } r ^ { - 3 } } \right) ^ { 2 }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Perform the operation and simplify. $( a - 14 ) ^ { 2 }$

Identify the correct union of intervals for the inequality. $x \leq - 16$ or $x > 5$

Factor the expression completely. $30 x ^ { 2 } - 13 x y - 56 y ^ { 2 }$

Factor the expression completely. $4 z ^ { 2 } + 28 z + 49$

Multiply the expression as you would multiply polynomials. $\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } \right) ^ { 2 }$

Factor the expression completely. $9 z ^ { 2 } + 42 z + 49$

Perform the multiplication and simplify. $( x - y ) ( 3 x + 14 y ) ^ { 2 }$

Rationalize the numerator and simplify. $\frac { \sqrt { 5 } } { 25 }$

Simplify the fraction. $\frac { 3 x - 9 } { x ^ { 2 } - 9 }$ Assume that the denominator is not 0 .

Perform the operations and simplify. $\left( 8 x ^ { 3 } - 3 x ^ { 2 } \right) + \left( 5 x ^ { 3 } - 3 x \right)$

Factor the expression completely. $56 x ^ { 2 } - 29 x y - 40 y ^ { 2 }$

Perform the division and write the answer without using negative exponents. $\frac { 100 x ^ { 5 } y ^ { 7 } - 60 x ^ { 2 } y ^ { 5 } + 20 x y } { 10 x ^ { 5 } y ^ { 4 } }$

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Exam 1: A Review of Basic Algebra

Perform the division and write the answer without using negative exponents. 400x5y7−240x2y5+80xy16x5y4\frac { 400 x ^ { 5 } y ^ { 7 } - 240 x ^ { 2 } y ^ { 5 } + 80 x y } { 16 x ^ { 5 } y ^ { 4 } }16x5y4400x5y7−240x2y5+80xy​

Simplify the fraction. xy+6x+8y+48x3+512\frac { x y + 6 x + 8 y + 48 } { x ^ { 3 } + 512 }x3+512xy+6x+8y+48​ Assume that denominator is not 0 .

Simplify each complex fraction. x+1−6xx+5+6x\frac { x + 1 - \frac { 6 } { x } } { x + 5 + \frac { 6 } { x } }x+5+x6​x+1−x6​​ Assume that no denominators are 0 .

How many natural numbers are there between -6.5 and 12.5 on the number line?

Multiply the expression as you would multiply polynomials. (x7/2+y9/2)2\left( x ^ { 7 / 2 } + y ^ { 9 / 2 } \right) ^ { 2 }(x7/2+y9/2)2

Perform the division.

Simplify the expression. (r5r−1r3r−3)2\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 3 } r ^ { - 3 } } \right) ^ { 2 }(r3r−3r5r−1​)2 Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Perform the operation and simplify. (a−14)2( a - 14 ) ^ { 2 }(a−14)2

Identify the correct union of intervals for the inequality. x≤−16x \leq - 16x≤−16 or x>5x > 5x>5

Factor the expression completely. 30x2−13xy−56y230 x ^ { 2 } - 13 x y - 56 y ^ { 2 }30x2−13xy−56y2

Factor the expression completely. 4z2+28z+494 z ^ { 2 } + 28 z + 494z2+28z+49

Multiply the expression as you would multiply polynomials. (x17/2+y7/2)2\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } \right) ^ { 2 }(x17/2+y7/2)2

Factor the expression completely. 9z2+42z+499 z ^ { 2 } + 42 z + 499z2+42z+49

Perform the multiplication and simplify. (x−y)(3x+14y)2( x - y ) ( 3 x + 14 y ) ^ { 2 }(x−y)(3x+14y)2

Rationalize the numerator and simplify. 525\frac { \sqrt { 5 } } { 25 }255​​

Simplify the fraction. 3x−9x2−9\frac { 3 x - 9 } { x ^ { 2 } - 9 }x2−93x−9​ Assume that the denominator is not 0 .

Perform the operations and simplify. (8x3−3x2)+(5x3−3x)\left( 8 x ^ { 3 } - 3 x ^ { 2 } \right) + \left( 5 x ^ { 3 } - 3 x \right)(8x3−3x2)+(5x3−3x)

Factor the expression completely. 56x2−29xy−40y256 x ^ { 2 } - 29 x y - 40 y ^ { 2 }56x2−29xy−40y2

Perform the division and write the answer without using negative exponents. 100x5y7−60x2y5+20xy10x5y4\frac { 100 x ^ { 5 } y ^ { 7 } - 60 x ^ { 2 } y ^ { 5 } + 20 x y } { 10 x ^ { 5 } y ^ { 4 } }10x5y4100x5y7−60x2y5+20xy​

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Perform the division and write the answer without using negative exponents. $\frac { 400 x ^ { 5 } y ^ { 7 } - 240 x ^ { 2 } y ^ { 5 } + 80 x y } { 16 x ^ { 5 } y ^ { 4 } }$

Simplify the fraction. $\frac { x y + 6 x + 8 y + 48 } { x ^ { 3 } + 512 }$ Assume that denominator is not 0 .

Simplify each complex fraction. $\frac { x + 1 - \frac { 6 } { x } } { x + 5 + \frac { 6 } { x } }$ Assume that no denominators are 0 .

Multiply the expression as you would multiply polynomials. $\left( x ^ { 7 / 2 } + y ^ { 9 / 2 } \right) ^ { 2 }$

Simplify the expression. $\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 3 } r ^ { - 3 } } \right) ^ { 2 }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Perform the operation and simplify. $( a - 14 ) ^ { 2 }$

Identify the correct union of intervals for the inequality. $x \leq - 16$ or $x > 5$

Factor the expression completely. $30 x ^ { 2 } - 13 x y - 56 y ^ { 2 }$

Factor the expression completely. $4 z ^ { 2 } + 28 z + 49$

Multiply the expression as you would multiply polynomials. $\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } \right) ^ { 2 }$

Factor the expression completely. $9 z ^ { 2 } + 42 z + 49$

Perform the multiplication and simplify. $( x - y ) ( 3 x + 14 y ) ^ { 2 }$

Rationalize the numerator and simplify. $\frac { \sqrt { 5 } } { 25 }$

Simplify the fraction. $\frac { 3 x - 9 } { x ^ { 2 } - 9 }$ Assume that the denominator is not 0 .

Perform the operations and simplify. $\left( 8 x ^ { 3 } - 3 x ^ { 2 } \right) + \left( 5 x ^ { 3 } - 3 x \right)$

Factor the expression completely. $56 x ^ { 2 } - 29 x y - 40 y ^ { 2 }$

Perform the division and write the answer without using negative exponents. $\frac { 100 x ^ { 5 } y ^ { 7 } - 60 x ^ { 2 } y ^ { 5 } + 20 x y } { 10 x ^ { 5 } y ^ { 4 } }$