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College Algebra : Review and Other Topics

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Example Questions

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Example Question #1 : Rational Exponents

Evaluate.

$144^{1/2}$

Possible Answers:

$\pm22$

$\pm12$

$\pm36$

Correct answer:

$\pm12$

Explanation:

Exponents raised to a power of <1 can be written as the root of the denominator.

So:

$144^{1/2} = \sqrt[2]{144}=\pm12$

Recall that a square root can give two answers, one positive and one negative.

$\\(-12)(-12)=144 \\(12)(12)=144$

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Example Question #1 : Rational Exponents

Evaluate

$8^{11/5}$

Possible Answers:

2.4

2.2

2.8

2.6

2.1

Correct answer:

2.2

Explanation:

$8^{11/5}$

The denominator of the exponent "N" is the same as the "N" root of that number.

$8^{11/5} = \sqrt[5]{8^{11}} = 2.2$

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Example Question #1 : Rational Exponents

Evaluate

$(7^{5/3})^{3/4}$

Possible Answers:

11.386

14.215

13.569

10.582

11.478

Correct answer:

11.386

Explanation:

This appears more complicated than it is.

$(7^{5/3})^{3/4}$ is really just X^Y where

$X=7^{5/3}$

and

y=3/4

Re-written this equation looks like

$(\sqrt[3]{7^5})^{3/4} = 1.667^{3/4}= \sqrt[4]{1.667^3} = 11.386$

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Example Question #1 : Rational Exponents

Evaluate

$17^{0.824}$

Possible Answers:

14.578

13.325

9.876

18.256

10.325

Correct answer:

10.325

Explanation:

$17^{0.824}$ can be seen as X^Y , in a scientific calculator use the X^Y button where Y=0.824 .

$17^{0.824}=10.325$

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Example Question #2 : Rational Exponents

Evaluate the given rational exponent:

$8^{\frac{2}{3}}$

Possible Answers:

Correct answer:

Explanation:

Rational exponents can be simplified by following this common rule:

$a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$

We can apply this concept to the given value in order to evaluate:

$\\8^{\frac{2}{3}}=\sqrt[3]{8^{2}}=\sqrt[3]{64}\\\sqrt[3]{64}=4$

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Example Question #11 : Rational Exponents

Solve for :

$81^{\frac{x}{4}}=27$

Possible Answers:

x=5

x=-1

x=3

$x=\frac{-1}{2}$

x=1

Correct answer:

x=3

Explanation:

We can use the given property of rational exponents to solve for :

$a^\frac{m}{n}=\sqrt[n]{a^m}$

$\\81^{\frac{x}{4}}=\sqrt[4]{81^{x}}=27\\27^{4}=81^x\\81^{x}=531,441\\81^{3}=531,441\\x=3$

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Example Question #11 : Rational Exponents

Solve for :

$32^{\frac{2}{x}}=4$

Possible Answers:

$x=\frac{-2}{3}$

x=5

x=1

$x=\frac{4}{3}$

x=3

Correct answer:

x=5

Explanation:

We can use the given property of rational exponents to solve for :

$a^{\frac{m}{n}}=\sqrt[n]{a^m}$

$\\32^{\frac{2}{x}}=\sqrt[x]{32^2}=4\\\sqrt[x]{1024}=4\\4^{x}=1024\\4^{5}=1024\\x=5$

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Example Question #31 : Review And Other Topics

Evaluate: $(625)^{\frac {1}{4}}$

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to understand what the fractional value in the exponent is.

A fractional exponent, $\frac {1}{n}$ , tells us that we must take the th root of the number.

In this case, we have $\frac {1}{4}$ , so we will take the 4th root of 625 .

Step 2: Calculate... $\sqrt_[4]{625}=5$

$\sqrt[4]{625}=\sqrt[4]{5*5*5*5}=5$

The answer is .

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Example Question #31 : Review And Other Topics

Simplfy:

$\frac{x^{3.78}}{x^{2.58}}$

Possible Answers:

$x^{1.2}$

$x^{1.3}$

$x^{1.1}$

Correct answer:

$x^{1.2}$

Explanation:

Treat this with regular exponent rules.

$\frac{x^{3.78}}{x^{2.58}}=x^{3.78-2.58}=x^{1.2}$

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Example Question #32 : Review And Other Topics

Simplify: $\frac{15x^2y^5c^3}{5xy^6c^3}$

Possible Answers:

$\frac{3x}{yc}$

$\frac{3x}{y}$

The answer is not present.

$\frac{3y}{x}$

3xy

Correct answer:

$\frac{3x}{y}$

Explanation:

$\frac{15x^2y^5c^3}{5xy^6c^3} \rightarrow 3xy^{-1}\rightarrow 3x*\frac{1}{y}=\boldsymbol{\frac{3x}{y}}$

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College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #1 : Rational Exponents

Example Question #1 : Rational Exponents

Example Question #1 : Rational Exponents

Example Question #1 : Rational Exponents

Example Question #2 : Rational Exponents

Example Question #11 : Rational Exponents

Example Question #11 : Rational Exponents

Example Question #31 : Review And Other Topics

Example Question #31 : Review And Other Topics

Example Question #32 : Review And Other Topics

All College Algebra Resources

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