Exam 10: Exponents and Radicals

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt { 32 a ^ { 2 } b } } { \sqrt { 11 a ^ { 3 } b ^ { 3 } } }$

(Multiple Choice)

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Question 41

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { 21 } { \sqrt { 21 } + 1 }$ Please enter your answer as a fraction.

(Short Answer)

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Question 42

The factors $a - b$ and $b - a$ are conjugates.

(True/False)

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Question 43

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $20 \sqrt { 247 } - 80 \sqrt { 221 }$

(Multiple Choice)

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Question 44

Simplify the numerical expression. $\frac { 1 } { 5 ^ { - 3 } }$

(Multiple Choice)

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Question 45

Change the radical to simplest radical form. $5 \sqrt { 180 }$

(Multiple Choice)

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Question 46

Find the indicated quotients. Express final results using positive integral exponents only. $\frac { 18 x ^ { - 4 } y ^ { - 9 } } { 9 x ^ { - 9 } y ^ { - 3 } }$ Please enter your answer as a fraction.

(Short Answer)

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Question 47

The equations $\sqrt { x + 1 } = 10$ and $\sqrt { 10 } = x + 1$ are examples of radical equations.

(True/False)

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Question 48

Perform the operation and express the answer in simplest radical form. $\sqrt { 5 } \sqrt [ 3 ] { 5 }$

(Short Answer)

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Question 49

Solve the equation. $\sqrt { 7 x } = 21$

(Short Answer)

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Question 50

Change the radical to simplest radical form. $\sqrt { \frac { 10 } { 7 } }$

(Multiple Choice)

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Question 51

Solve the equation. $\sqrt { n + 10 } = n + 10$

(Multiple Choice)

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Question 52

Simplify the numerical expression. ( 3 2 . 7 -1 ) 2

(Multiple Choice)

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Question 53

Solve the equation. $\sqrt { n - 3 } + \sqrt { n + 5 } = 2 \sqrt { n }$

(Multiple Choice)

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Question 54

Solve the equation. $\sqrt { 5 y + 39 } - 7 = 0$

(Short Answer)

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Question 55

Simplify the numerical expression. $\frac { 1 } { 5 ^ { - 2 } }$

(Short Answer)

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Question 56

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 36 x ^ { 9 } y ^ { 4 } }$

(Short Answer)

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Question 57

Solve the equation. $\sqrt { 4 y + 16 } - 6 = 0$

(Multiple Choice)

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Question 58

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $- 760 - 32 \sqrt { 247 }$

(Multiple Choice)

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Question 59

Express the following as a single fraction involving positive exponents only. 4 x ^{- 3} - 5 x ^{- 7}

(Multiple Choice)

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Question 60

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt { 32 a ^ { 2 } b } } { \sqrt { 11 a ^ { 3 } b ^ { 3 } } }$

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { 21 } { \sqrt { 21 } + 1 }$ Please enter your answer as a fraction.

The factors $a - b$ and $b - a$ are conjugates.

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $20 \sqrt { 247 } - 80 \sqrt { 221 }$

Simplify the numerical expression. $\frac { 1 } { 5 ^ { - 3 } }$

Change the radical to simplest radical form. $5 \sqrt { 180 }$

Find the indicated quotients. Express final results using positive integral exponents only. $\frac { 18 x ^ { - 4 } y ^ { - 9 } } { 9 x ^ { - 9 } y ^ { - 3 } }$ Please enter your answer as a fraction.

The equations $\sqrt { x + 1 } = 10$ and $\sqrt { 10 } = x + 1$ are examples of radical equations.

Perform the operation and express the answer in simplest radical form. $\sqrt { 5 } \sqrt [ 3 ] { 5 }$

Solve the equation. $\sqrt { 7 x } = 21$

Change the radical to simplest radical form. $\sqrt { \frac { 10 } { 7 } }$

Solve the equation. $\sqrt { n + 10 } = n + 10$

Simplify the numerical expression. ( 3 2 . 7 -1 ) 2

Solve the equation. $\sqrt { n - 3 } + \sqrt { n + 5 } = 2 \sqrt { n }$

Solve the equation. $\sqrt { 5 y + 39 } - 7 = 0$

Simplify the numerical expression. $\frac { 1 } { 5 ^ { - 2 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 36 x ^ { 9 } y ^ { 4 } }$

Solve the equation. $\sqrt { 4 y + 16 } - 6 = 0$

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $- 760 - 32 \sqrt { 247 }$

Express the following as a single fraction involving positive exponents only. 4 x ^{- 3} - 5 x ^{- 7}

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Quadratic Equations and Inequalities

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

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

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Exam 10: Exponents and Radicals

Express the following expression in simplest radical form. All variables represent positive real numbers. 32a2b11a3b3\frac { \sqrt { 32 a ^ { 2 } b } } { \sqrt { 11 a ^ { 3 } b ^ { 3 } } }11a3b3​32a2b​​

Rationalize the denominator and simplify. All variables represent positive real numbers. 2121+1\frac { 21 } { \sqrt { 21 } + 1 }21​+121​ Please enter your answer as a fraction.

The factors a−ba - ba−b and b−ab - ab−a are conjugates.

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - 20247−8022120 \sqrt { 247 } - 80 \sqrt { 221 }20247​−80221​

Simplify the numerical expression. 15−3\frac { 1 } { 5 ^ { - 3 } }5−31​

Change the radical to simplest radical form. 51805 \sqrt { 180 }5180​

Find the indicated quotients. Express final results using positive integral exponents only. 18x−4y−99x−9y−3\frac { 18 x ^ { - 4 } y ^ { - 9 } } { 9 x ^ { - 9 } y ^ { - 3 } }9x−9y−318x−4y−9​ Please enter your answer as a fraction.

The equations x+1=10\sqrt { x + 1 } = 10x+1​=10 and 10=x+1\sqrt { 10 } = x + 110​=x+1 are examples of radical equations.

Perform the operation and express the answer in simplest radical form. 553\sqrt { 5 } \sqrt [ 3 ] { 5 }5​35​

Solve the equation. 7x=21\sqrt { 7 x } = 217x​=21

Change the radical to simplest radical form. 107\sqrt { \frac { 10 } { 7 } }710​​

Solve the equation. n+10=n+10\sqrt { n + 10 } = n + 10n+10​=n+10

Simplify the numerical expression. ( 3 2 . 7 -1 ) 2

Solve the equation. n−3+n+5=2n\sqrt { n - 3 } + \sqrt { n + 5 } = 2 \sqrt { n }n−3​+n+5​=2n​

Solve the equation. 5y+39−7=0\sqrt { 5 y + 39 } - 7 = 05y+39​−7=0

Simplify the numerical expression. 15−2\frac { 1 } { 5 ^ { - 2 } }5−21​

Express the following expression in simplest radical form. All variables represent positive real numbers. 36x9y4\sqrt { 36 x ^ { 9 } y ^ { 4 } }36x9y4​

Solve the equation. 4y+16−6=0\sqrt { 4 y + 16 } - 6 = 04y+16​−6=0

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - −760−32247- 760 - 32 \sqrt { 247 }−760−32247​

Express the following as a single fraction involving positive exponents only. 4 x - 3 - 5 x - 7

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Quadratic Equations and Inequalities

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

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt { 32 a ^ { 2 } b } } { \sqrt { 11 a ^ { 3 } b ^ { 3 } } }$

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { 21 } { \sqrt { 21 } + 1 }$ Please enter your answer as a fraction.

The factors $a - b$ and $b - a$ are conjugates.

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $20 \sqrt { 247 } - 80 \sqrt { 221 }$

Simplify the numerical expression. $\frac { 1 } { 5 ^ { - 3 } }$

Change the radical to simplest radical form. $5 \sqrt { 180 }$

Find the indicated quotients. Express final results using positive integral exponents only. $\frac { 18 x ^ { - 4 } y ^ { - 9 } } { 9 x ^ { - 9 } y ^ { - 3 } }$ Please enter your answer as a fraction.

The equations $\sqrt { x + 1 } = 10$ and $\sqrt { 10 } = x + 1$ are examples of radical equations.

Perform the operation and express the answer in simplest radical form. $\sqrt { 5 } \sqrt [ 3 ] { 5 }$

Solve the equation. $\sqrt { 7 x } = 21$

Change the radical to simplest radical form. $\sqrt { \frac { 10 } { 7 } }$

Solve the equation. $\sqrt { n + 10 } = n + 10$

Solve the equation. $\sqrt { n - 3 } + \sqrt { n + 5 } = 2 \sqrt { n }$

Solve the equation. $\sqrt { 5 y + 39 } - 7 = 0$

Simplify the numerical expression. $\frac { 1 } { 5 ^ { - 2 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 36 x ^ { 9 } y ^ { 4 } }$

Solve the equation. $\sqrt { 4 y + 16 } - 6 = 0$

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $- 760 - 32 \sqrt { 247 }$

Express the following as a single fraction involving positive exponents only. 4 x ^{- 3} - 5 x ^{- 7}