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College Algebra : College Algebra

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5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : Integer Exponents

$\frac{x^{6}}{x^{3}}=$

Possible Answers:

$x^{12}$

x^3

$x^{1/2}$

x^9

$x^{27}$

Correct answer:

x^3

Explanation:

When similar terms raised to n are divided, subtract the exponents. Thus

$\frac{x^{6}}{x^{3}}=x^{6-3}=x^3$

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Example Question #13 : Integer Exponents

$\frac{x^{10}}{x^{6}}=$

Possible Answers:

x^4

$x^{16}$

60x

$x^{60}$

$\frac{x^5}{x^3}$

Correct answer:

x^4

Explanation:

When similar terms raised to n are divided, subtract the exponents. Thus

$\frac{x^{10}}{x^{6}}=x^{10-6}=x^4$

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Example Question #14 : Integer Exponents

$\frac{x^{12}}{x^{7}}=$

Possible Answers:

$x^{19}$

$x^{1.7}$

$x^{72}$

x^5

$x^{84}$

Correct answer:

x^5

Explanation:

When similar terms raised to n are divided, subtract the exponents. Thus

$\frac{x^{12}}{x^{7}}=x^{12-7}=x^5$

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Example Question #15 : Integer Exponents

(x^4)^6=

Possible Answers:

$x^{24}$

$x^{12}$

$x^{-2}$

x^2

$x^{10}$

Correct answer:

$x^{24}$

Explanation:

When a term with an exponent is raised to another power, multiply the exponents. Thus

$(x^4)^6=x^{4*6}=x^{24}$

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Example Question #16 : Integer Exponents

(x^3)^2=

Possible Answers:

x^6

x^5

$x^{2/3}$

Correct answer:

x^6

Explanation:

When a term with an exponent is raised to another power, multiply the exponents. Thus

$(x^3)^2=x^{3*2}=x^6$

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Example Question #17 : Integer Exponents

(x^2)^5=

Possible Answers:

$x^{-3}$

$x^{10}$

$x^{7}$

x^3

5x^2

Correct answer:

$x^{10}$

Explanation:

When a term with an exponent is raised to another power, multiply the exponents. Thus

$(x^2)^5=x^{2*5}=x^{10}$

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Example Question #18 : Integer Exponents

$\sqrt[5]{x^{10}}=$

Possible Answers:

x^2

$10x^{5}$

x^5

$x^{50}$

$x^{15}$

Correct answer:

x^2

Explanation:

The root of x^y is y/n . Thus

$\sqrt[5]{x^{10}}=x^{10/5}=x^2$

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Example Question #19 : Integer Exponents

$\sqrt[3]{x^{21}}=$

Possible Answers:

x^7

$x^{24}$

$x^{18}$

$3x^{21}$

$x^{63}$

Correct answer:

x^7

Explanation:

The root of x^y is y/n . Thus

$\sqrt[3]{x^{21}}=x^{21/3}=x^7$

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Example Question #20 : Review And Other Topics

$\sqrt[4]{x^{64}}=$

Possible Answers:

$x^{16}$

$\frac{x^{64}}{4}$

$x^{68}$

$x^{60}$

$6x^{10}$

Correct answer:

$x^{16}$

Explanation:

The root of x^y is $x^{\frac{y}{n}}$ thus

$\sqrt[4]{x^{64}}=x^{64/4}=x^{16}$

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Example Question #300 : College Algebra

Solve: $2(5^{-3})$

Possible Answers:

$-\frac{2}{125}$

$\frac{1}{1000}$

$-\frac{1}{30}$

$\frac{2}{125}$

Correct answer:

$\frac{2}{125}$

Explanation:

Evaluate the negative exponential first.

$5^{-3} =\frac{1}{5^3} = \frac{1}{125}$

Replace the fraction.

$2(5^{-3}) =2 (\frac{1}{125})= \frac{2}{125}$

The answer is: $\frac{2}{125}$

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College Algebra : College Algebra

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #12 : Integer Exponents

Example Question #13 : Integer Exponents

Example Question #14 : Integer Exponents

Example Question #15 : Integer Exponents

Example Question #16 : Integer Exponents

Example Question #17 : Integer Exponents

Example Question #18 : Integer Exponents

Example Question #19 : Integer Exponents

Example Question #20 : Review And Other Topics

Example Question #300 : College Algebra

All College Algebra Resources

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