Exam 1: A Review of Basic Algebra

We can often multiply and divide radicals with different indexes.For example: $\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$ Use this idea to write the following expression as a single radical. $\sqrt { 3 } \sqrt [ 3 ] { 3 }$

(Multiple Choice)

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Question 121

Perform the operations and simplify. $\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }$ Assume that no denominators are 0 .

(Multiple Choice)

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Question 122

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

(Multiple Choice)

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Question 123

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

(Multiple Choice)

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Question 124

Select the correct representation of the inequality in interval notation. $x \leq 3$

(Multiple Choice)

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Question 125

Perform the operations and simplify. $\frac { x + 8 } { x ^ { 2 } + 11 x + 24 } + \frac { x } { x ^ { 2 } - 9 }$ Assume that no denominators are 0 .

(Multiple Choice)

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Question 126

Factor the expression completely. $4 x ^ { 3 } + 4 x ^ { 2 } - 7 x - 7$

(Multiple Choice)

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Question 127

Perform division and write the answer without using negative exponents. $\frac { - 12 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 3 x ^ { 9 } y ^ { 6 } z ^ { 0 } }$

(Multiple Choice)

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Question 128

Simplify the fraction. $\frac { 8 x - 64 } { x ^ { 2 } - 64 }$ Assume that the denominator is not 0 .

(Multiple Choice)

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Question 129

Simplify the expression. $\frac { \left( 8 ^ { - 2 } z ^ { - 5 } y \right) ^ { - 2 } } { \left( 5 y ^ { 2 } z ^ { - 5 } \right) ^ { 5 } \left( 5 y z ^ { - 5 } \right) ^ { - 1 } }$ 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 130

Factor the expression completely. $z ^ { 2 } + 4 z + 4 - 144 y ^ { 2 }$

(Multiple Choice)

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Question 131

Simplify the expression. $\left( \frac { r ^ { 4 } r ^ { - 2 } } { r ^ { 4 } r ^ { - 4 } } \right) ^ { 5 }$ 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 132

Perform the operation and simplify. $( a - 15 ) ^ { 2 }$

(Multiple Choice)

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Question 133

Multiply the expression as you would multiply polynomials. $\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)$

(Multiple Choice)

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Question 134

Simplify the expression. $\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 6 } r ^ { - 6 } } \right) ^ { 4 }$ 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 135

Perform division and write the answer without using negative exponents. $\frac { - 56 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 14 x ^ { 9 } y ^ { 6 } z ^ { 0 } }$

(Multiple Choice)

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Question 136

Simplify the complex fraction. $\frac { \frac { 2 x ^ { 2 } } { y ^ { 3 } } } { \frac { 4 x ^ { 4 } z ^ { 3 } } { y ^ { 5 } } }$ Assume that the denominators are not 0.

(Multiple Choice)

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Question 137

Perform the operations and simplify. $\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }$ Assume that no denominators are 0 .

(Multiple Choice)

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Question 138

Identify the correct union of intervals for the inequality. $x \leq - 14$ or $x > 10$

(Multiple Choice)

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Question 139

Simplify the expression. $( - 14 x ) ^ { 0 }$ Write the answer without using exponents.

(Multiple Choice)

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Question 140

Perform the operations and simplify. $\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }$ Assume that no denominators are 0 .

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

Select the correct representation of the inequality in interval notation. $x \leq 3$

Perform the operations and simplify. $\frac { x + 8 } { x ^ { 2 } + 11 x + 24 } + \frac { x } { x ^ { 2 } - 9 }$ Assume that no denominators are 0 .

Factor the expression completely. $4 x ^ { 3 } + 4 x ^ { 2 } - 7 x - 7$

Perform division and write the answer without using negative exponents. $\frac { - 12 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 3 x ^ { 9 } y ^ { 6 } z ^ { 0 } }$

Simplify the fraction. $\frac { 8 x - 64 } { x ^ { 2 } - 64 }$ Assume that the denominator is not 0 .

Factor the expression completely. $z ^ { 2 } + 4 z + 4 - 144 y ^ { 2 }$

Simplify the expression. $\left( \frac { r ^ { 4 } r ^ { - 2 } } { r ^ { 4 } r ^ { - 4 } } \right) ^ { 5 }$ 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. $( a - 15 ) ^ { 2 }$

Multiply the expression as you would multiply polynomials. $\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)$

Simplify the expression. $\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 6 } r ^ { - 6 } } \right) ^ { 4 }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Perform division and write the answer without using negative exponents. $\frac { - 56 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 14 x ^ { 9 } y ^ { 6 } z ^ { 0 } }$

Simplify the complex fraction. $\frac { \frac { 2 x ^ { 2 } } { y ^ { 3 } } } { \frac { 4 x ^ { 4 } z ^ { 3 } } { y ^ { 5 } } }$ Assume that the denominators are not 0.

Perform the operations and simplify. $\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }$ Assume that no denominators are 0 .

Identify the correct union of intervals for the inequality. $x \leq - 14$ or $x > 10$

Simplify the expression. $( - 14 x ) ^ { 0 }$ Write the answer without using exponents.

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 operations and simplify. 1x−4+3x+4−3x−4x2−16\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }x−41​+x+43​−x2−163x−4​ Assume that no denominators are 0 .

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. 2xy54+y512xy4−2xy54\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }42xy5​+y4512xy​−42xy5​

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. 2xy54+y512xy4−2xy54\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }42xy5​+y4512xy​−42xy5​

Select the correct representation of the inequality in interval notation. x≤3x \leq 3x≤3

Perform the operations and simplify. x+8x2+11x+24+xx2−9\frac { x + 8 } { x ^ { 2 } + 11 x + 24 } + \frac { x } { x ^ { 2 } - 9 }x2+11x+24x+8​+x2−9x​ Assume that no denominators are 0 .

Factor the expression completely. 4x3+4x2−7x−74 x ^ { 3 } + 4 x ^ { 2 } - 7 x - 74x3+4x2−7x−7

Perform division and write the answer without using negative exponents. −12x6y4z93x9y6z0\frac { - 12 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 3 x ^ { 9 } y ^ { 6 } z ^ { 0 } }3x9y6z0−12x6y4z9​

Simplify the fraction. 8x−64x2−64\frac { 8 x - 64 } { x ^ { 2 } - 64 }x2−648x−64​ Assume that the denominator is not 0 .

Factor the expression completely. z2+4z+4−144y2z ^ { 2 } + 4 z + 4 - 144 y ^ { 2 }z2+4z+4−144y2

Simplify the expression. (r4r−2r4r−4)5\left( \frac { r ^ { 4 } r ^ { - 2 } } { r ^ { 4 } r ^ { - 4 } } \right) ^ { 5 }(r4r−4r4r−2​)5 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−15)2( a - 15 ) ^ { 2 }(a−15)2

Multiply the expression as you would multiply polynomials. (a19/2+b9/2)(a19/2−b9/2)\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)(a19/2+b9/2)(a19/2−b9/2)

Simplify the expression. (r5r−1r6r−6)4\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 6 } r ^ { - 6 } } \right) ^ { 4 }(r6r−6r5r−1​)4 Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Perform division and write the answer without using negative exponents. −56x6y4z914x9y6z0\frac { - 56 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 14 x ^ { 9 } y ^ { 6 } z ^ { 0 } }14x9y6z0−56x6y4z9​

Simplify the complex fraction. 2x2y34x4z3y5\frac { \frac { 2 x ^ { 2 } } { y ^ { 3 } } } { \frac { 4 x ^ { 4 } z ^ { 3 } } { y ^ { 5 } } }y54x4z3​y32x2​​ Assume that the denominators are not 0.

Perform the operations and simplify. 1x−4+3x+4−3x−4x2−16\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }x−41​+x+43​−x2−163x−4​ Assume that no denominators are 0 .

Identify the correct union of intervals for the inequality. x≤−14x \leq - 14x≤−14 or x>10x > 10x>10

Simplify the expression. (−14x)0( - 14 x ) ^ { 0 }(−14x)0 Write the answer without using exponents.

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 operations and simplify. $\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }$ Assume that no denominators are 0 .

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

Select the correct representation of the inequality in interval notation. $x \leq 3$

Perform the operations and simplify. $\frac { x + 8 } { x ^ { 2 } + 11 x + 24 } + \frac { x } { x ^ { 2 } - 9 }$ Assume that no denominators are 0 .

Factor the expression completely. $4 x ^ { 3 } + 4 x ^ { 2 } - 7 x - 7$

Perform division and write the answer without using negative exponents. $\frac { - 12 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 3 x ^ { 9 } y ^ { 6 } z ^ { 0 } }$

Simplify the fraction. $\frac { 8 x - 64 } { x ^ { 2 } - 64 }$ Assume that the denominator is not 0 .

Factor the expression completely. $z ^ { 2 } + 4 z + 4 - 144 y ^ { 2 }$

Simplify the expression. $\left( \frac { r ^ { 4 } r ^ { - 2 } } { r ^ { 4 } r ^ { - 4 } } \right) ^ { 5 }$ 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. $( a - 15 ) ^ { 2 }$

Multiply the expression as you would multiply polynomials. $\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)$

Simplify the expression. $\left( \frac { r ^ { 5 } r ^ { - 1 } } { r ^ { 6 } r ^ { - 6 } } \right) ^ { 4 }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Perform division and write the answer without using negative exponents. $\frac { - 56 x ^ { 6 } y ^ { 4 } z ^ { 9 } } { 14 x ^ { 9 } y ^ { 6 } z ^ { 0 } }$

Simplify the complex fraction. $\frac { \frac { 2 x ^ { 2 } } { y ^ { 3 } } } { \frac { 4 x ^ { 4 } z ^ { 3 } } { y ^ { 5 } } }$ Assume that the denominators are not 0.

Perform the operations and simplify. $\frac { 1 } { x - 4 } + \frac { 3 } { x + 4 } - \frac { 3 x - 4 } { x ^ { 2 } - 16 }$ Assume that no denominators are 0 .

Identify the correct union of intervals for the inequality. $x \leq - 14$ or $x > 10$

Simplify the expression. $( - 14 x ) ^ { 0 }$ Write the answer without using exponents.