Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 4 } } { x ^ { - 11 } }$

(Multiple Choice)

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Question 181

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $( x - 11 ) \left( x ^ { 2 } + 5 x - 8 \right)$

(Multiple Choice)

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Question 182

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 49 }$

(Multiple Choice)

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Question 183

Simplify the radical expression. Assume all variables represent positive real numbers. - $( 2 \sqrt { 11 } + 6 ) ^ { 2 }$

(Multiple Choice)

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Question 184

Completely factor the polynomial or state that the polynomial is prime. - $15 x ^ { 4 } - 14 x ^ { 2 } - 8$

(Multiple Choice)

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Question 185

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $(x+3) ^ { 3 }$

(Multiple Choice)

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Question 186

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 8 x ^ { 4 } - 5 x ^ { 2 } \right) + \left( 4 x ^ { 4 } + 2 x ^ { 2 } \right)$

(Multiple Choice)

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Question 187

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 13 x ^ { 4 } + 2 x ^ { 2 } \right) - \left( - 5 x ^ { 4 } + 2 x ^ { 2 } \right)$

(Multiple Choice)

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Question 188

Completely factor the polynomial or state that the polynomial is prime. - $343 x ^ { 3 } + 512$

(Multiple Choice)

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Question 189

Simplify the expression using the order of operations. - $10 ^ { 2 } - 5 \cdot 2$

(Multiple Choice)

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Question 190

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $1296 ^ { 1 / 4 }$

(Multiple Choice)

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Question 191

Use the distributive property to multiply the given expressions. - $( m + 8 - 3 n ) 2$

(Multiple Choice)

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Question 192

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( 16 x ^ { 8 } y ^ { 4 } \right) ^ { 1 / 2 }$

(Multiple Choice)

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Question 193

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 x ^ { 2 } } { x - 1 } - \frac { 8 x } { x - 1 }$

(Multiple Choice)

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Question 194

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { x + 8 } { x - 8 } + \frac { x - 8 } { x + 8 } } { \frac { x + 8 } { x - 8 } - \frac { x - 8 } { x + 8 } }$

(Multiple Choice)

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Question 195

List all the elements of B that belong to the given set. - $B = \left\{ 4 , \sqrt { 7 } , - 23,0 , \frac { 4 } { 9 } , - \frac { 9 } { 4 } , 2.2 \right\}$ Natural numbers

(Multiple Choice)

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Question 196

List all the elements of B that belong to the given set. - $B = \left\{ 3 , \sqrt { 5 } , - 17,0 , \frac { 0 } { 2 } , 0.47 \right\}$ Rational numbers

(Multiple Choice)

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Question 197

Determine whether the expression is a monomial. If it is a monomial, state the coefficient and degree. - $6 x ^ { 5 } - 3$

(Multiple Choice)

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Question 198

Completely factor the polynomial or state that the polynomial is prime. - $15 x ^ { 2 } - 65 x - 50$

(Multiple Choice)

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Question 199

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 1 - \frac { 4 } { x } } { x - \frac { 16 } { x } }$

(Multiple Choice)

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Question 200

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 4 } } { x ^ { - 11 } }$

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $( x - 11 ) \left( x ^ { 2 } + 5 x - 8 \right)$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 49 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $( 2 \sqrt { 11 } + 6 ) ^ { 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $15 x ^ { 4 } - 14 x ^ { 2 } - 8$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $(x+3) ^ { 3 }$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 8 x ^ { 4 } - 5 x ^ { 2 } \right) + \left( 4 x ^ { 4 } + 2 x ^ { 2 } \right)$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 13 x ^ { 4 } + 2 x ^ { 2 } \right) - \left( - 5 x ^ { 4 } + 2 x ^ { 2 } \right)$

Completely factor the polynomial or state that the polynomial is prime. - $343 x ^ { 3 } + 512$

Simplify the expression using the order of operations. - $10 ^ { 2 } - 5 \cdot 2$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $1296 ^ { 1 / 4 }$

Use the distributive property to multiply the given expressions. - $( m + 8 - 3 n ) 2$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( 16 x ^ { 8 } y ^ { 4 } \right) ^ { 1 / 2 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 x ^ { 2 } } { x - 1 } - \frac { 8 x } { x - 1 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { x + 8 } { x - 8 } + \frac { x - 8 } { x + 8 } } { \frac { x + 8 } { x - 8 } - \frac { x - 8 } { x + 8 } }$

List all the elements of B that belong to the given set. - $B = \left\{ 4 , \sqrt { 7 } , - 23,0 , \frac { 4 } { 9 } , - \frac { 9 } { 4 } , 2.2 \right\}$ Natural numbers

List all the elements of B that belong to the given set. - $B = \left\{ 3 , \sqrt { 5 } , - 17,0 , \frac { 0 } { 2 } , 0.47 \right\}$ Rational numbers

Determine whether the expression is a monomial. If it is a monomial, state the coefficient and degree. - $6 x ^ { 5 } - 3$

Completely factor the polynomial or state that the polynomial is prime. - $15 x ^ { 2 } - 65 x - 50$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 1 - \frac { 4 } { x } } { x - \frac { 16 } { x } }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - x−4x−11\frac { x ^ { - 4 } } { x ^ { - 11 } }x−11x−4​

Perform the indicated operations. Express the answer as a single polynomial in standard form. - (x−11)(x2+5x−8)( x - 11 ) \left( x ^ { 2 } + 5 x - 8 \right)(x−11)(x2+5x−8)

Simplify the radical expression. Assume all variables represent positive real numbers. - 49\sqrt { 49 }49​

Simplify the radical expression. Assume all variables represent positive real numbers. - (211+6)2( 2 \sqrt { 11 } + 6 ) ^ { 2 }(211​+6)2

Completely factor the polynomial or state that the polynomial is prime. - 15x4−14x2−815 x ^ { 4 } - 14 x ^ { 2 } - 815x4−14x2−8

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - (x+3)3(x+3) ^ { 3 } (x+3)3

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - (8x4−5x2)+(4x4+2x2)\left( 8 x ^ { 4 } - 5 x ^ { 2 } \right) + \left( 4 x ^ { 4 } + 2 x ^ { 2 } \right)(8x4−5x2)+(4x4+2x2)

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - (13x4+2x2)−(−5x4+2x2)\left( 13 x ^ { 4 } + 2 x ^ { 2 } \right) - \left( - 5 x ^ { 4 } + 2 x ^ { 2 } \right)(13x4+2x2)−(−5x4+2x2)

Completely factor the polynomial or state that the polynomial is prime. - 343x3+512343 x ^ { 3 } + 512343x3+512

Simplify the expression using the order of operations. - 102−5⋅210 ^ { 2 } - 5 \cdot 2102−5⋅2

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - 12961/41296 ^ { 1 / 4 }12961/4

Use the distributive property to multiply the given expressions. - (m+8−3n)2( m + 8 - 3 n ) 2(m+8−3n)2

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - (16x8y4)1/2\left( 16 x ^ { 8 } y ^ { 4 } \right) ^ { 1 / 2 }(16x8y4)1/2

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 8x2x−1−8xx−1\frac { 8 x ^ { 2 } } { x - 1 } - \frac { 8 x } { x - 1 }x−18x2​−x−18x​

List all the elements of B that belong to the given set. - B={4,7,−23,0,49,−94,2.2}B = \left\{ 4 , \sqrt { 7 } , - 23,0 , \frac { 4 } { 9 } , - \frac { 9 } { 4 } , 2.2 \right\}B={4,7​,−23,0,94​,−49​,2.2} Natural numbers

List all the elements of B that belong to the given set. - B={3,5,−17,0,02,0.47}B = \left\{ 3 , \sqrt { 5 } , - 17,0 , \frac { 0 } { 2 } , 0.47 \right\}B={3,5​,−17,0,20​,0.47} Rational numbers

Determine whether the expression is a monomial. If it is a monomial, state the coefficient and degree. - 6x5−36 x ^ { 5 } - 36x5−3

Completely factor the polynomial or state that the polynomial is prime. - 15x2−65x−5015 x ^ { 2 } - 65 x - 5015x2−65x−50

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 1−4xx−16x\frac { 1 - \frac { 4 } { x } } { x - \frac { 16 } { x } }x−x16​1−x4​​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 4 } } { x ^ { - 11 } }$

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $( x - 11 ) \left( x ^ { 2 } + 5 x - 8 \right)$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 49 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $( 2 \sqrt { 11 } + 6 ) ^ { 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $15 x ^ { 4 } - 14 x ^ { 2 } - 8$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $(x+3) ^ { 3 }$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 8 x ^ { 4 } - 5 x ^ { 2 } \right) + \left( 4 x ^ { 4 } + 2 x ^ { 2 } \right)$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 13 x ^ { 4 } + 2 x ^ { 2 } \right) - \left( - 5 x ^ { 4 } + 2 x ^ { 2 } \right)$

Completely factor the polynomial or state that the polynomial is prime. - $343 x ^ { 3 } + 512$

Simplify the expression using the order of operations. - $10 ^ { 2 } - 5 \cdot 2$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $1296 ^ { 1 / 4 }$

Use the distributive property to multiply the given expressions. - $( m + 8 - 3 n ) 2$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( 16 x ^ { 8 } y ^ { 4 } \right) ^ { 1 / 2 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 x ^ { 2 } } { x - 1 } - \frac { 8 x } { x - 1 }$

List all the elements of B that belong to the given set. - $B = \left\{ 4 , \sqrt { 7 } , - 23,0 , \frac { 4 } { 9 } , - \frac { 9 } { 4 } , 2.2 \right\}$ Natural numbers

List all the elements of B that belong to the given set. - $B = \left\{ 3 , \sqrt { 5 } , - 17,0 , \frac { 0 } { 2 } , 0.47 \right\}$ Rational numbers

Determine whether the expression is a monomial. If it is a monomial, state the coefficient and degree. - $6 x ^ { 5 } - 3$

Completely factor the polynomial or state that the polynomial is prime. - $15 x ^ { 2 } - 65 x - 50$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 1 - \frac { 4 } { x } } { x - \frac { 16 } { x } }$