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College Algebra : Rational Exponents

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Example Questions

Example Question #11 : Rational Exponents

Solve for :

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

Possible Answers:

x=3

x=1

x=5

x=-1

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

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 #31 : Review And Other Topics

Solve for :

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

Possible Answers:

x=1

x=5

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

x=3

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

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 #32 : 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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College Algebra : Rational Exponents

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #11 : Rational Exponents

Example Question #31 : Review And Other Topics

Example Question #32 : Review And Other Topics

All College Algebra Resources

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