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Algebra II : Fractional Exponents

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Example Question #1 : Rational Exponents

Which of the following is equivalent to $b^{\frac{4}{5}}$ ?

Possible Answers:

$\sqrt[4]{b^5}$

$\sqrt[5]{b^4}$

$\sqrt[4]{b^{-5}}$

5b^4

Correct answer:

$\sqrt[5]{b^4}$

Explanation:

Which of the following is equivalent to $b^{\frac{4}{5}}$ ?

When dealing with fractional exponents, keep the following in mind: The numerator is making the base bigger, so treat it like a regular exponent. The denominator is making the base smaller, so it must be the root you are taking.

This means that $b^{\frac{4}{5}}$ is equal to the fifth root of b to the fourth. Perhaps a bit confusing, but it means that we will keep b^4 , but put the whole thing under $\sqrt[5]{b}$ .

So if we put it together we get:

$\sqrt[5]{b^4}$

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Example Question #11 : Fractional Exponents

Evaluate $2^{\frac{1}2{}}$

Possible Answers:

$\frac{\sqrt{2}}2{}$

$\sqrt{2}$

$\frac{1}{4}$

Correct answer:

$\sqrt{2}$

Explanation:

When dealing with fractional exponents, remember this form:

$\sqrt[a]{x^n}$ is the index of the radical which is also the denominator of the fraction, represents the base of the exponent, and is the power the base is raised to. That value is the numerator of the fraction.

$2^{\frac{1}{2}}=\sqrt[2]{2^1}=\sqrt{2}$

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Example Question #12 : Fractional Exponents

Evaluate $3^{\frac{1}{3}}$

Possible Answers:

$\sqrt[3]{3}$

$\sqrt{3}$

$\frac{\sqrt[3]{3}}{3}$

$\frac{1}{27}$

Correct answer:

$\sqrt[3]{3}$

Explanation:

When dealing with fractional exponents, remember this form:

$3^{\frac{1}{3}}=\sqrt[3]{3^1}=\sqrt[3]{3}$

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Example Question #13 : Fractional Exponents

Evaluate $4^{\frac{2}{3}}$

Possible Answers:

$\frac{\sqrt[3]{16}}{2}$

$\frac{\sqrt[3]{4}}{2}$

$\sqrt[3]{16}$

Correct answer:

$\sqrt[3]{16}$

Explanation:

When dealing with fractional exponents, remember this form:

$4^{\frac{2}{3}}=\sqrt[3]{4^2}=\sqrt[3]{16}$

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Example Question #14 : Fractional Exponents

Evaluate $8^{\frac{1}{3}}$

Possible Answers:

$\sqrt[3]{3}$

$\sqrt[3]{2}$

$\sqrt{2}$

Correct answer:

Explanation:

When dealing with fractional exponents, remember this form:

$8^{\frac{1}{3}}=\sqrt[3]{8^1}=2$

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Example Question #15 : Fractional Exponents

Evaluate $\frac{1}{2}^{\frac{1}{2}}$

Possible Answers:

$\frac{\sqrt{2}}{4}$

$\frac{1}{2}$

$\sqrt{2}$

$\frac{\sqrt{2}}{2}$

$\frac{1}{4}$

Correct answer:

$\frac{\sqrt{2}}{2}$

Explanation:

When dealing with fractional exponents, remember this form:

$\frac{1}{2}^{\frac{1}{2}}=\sqrt[2]{\frac{1}{2}^1}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}$ To get rid of the radical, just multiply top and bottom by the radical.

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Example Question #16 : Fractional Exponents

Evaluate $\frac{1}{3}^{\frac{2}{3}}$

Possible Answers:

$\sqrt[3]{\frac{1}{9}}$

$\frac{\sqrt[3]{\frac{1}{9}}}{3}$

$\frac{2\sqrt[3]{\frac{1}{9}}}{3}$

$\frac{2}{9}$

$\frac{1}{3}$

Correct answer:

$\sqrt[3]{\frac{1}{9}}$

Explanation:

When dealing with fractional exponents, remember this form:

$\frac{1}{3}^{\frac{2}{3}}=\sqrt[3]{\frac{1}{3}^2}=\sqrt[3]{\frac{1}{9}}$

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Example Question #17 : Fractional Exponents

Evaluate $-\frac{1}{4}^{\frac{1}{2}}$

Possible Answers:

$\frac{1}{2}$

Does not exist

$-\frac{1}{2}$

Correct answer:

$-\frac{1}{2}$

Explanation:

When dealing with fractional exponents, remember this form:

$-\frac{1}{4}^{\frac{1}{2}}=-\sqrt[2]{\frac{1}{4}^1}=-\frac{1}{{2}}$ Remember to keep the negative on the outside. The exponent comes first followed by the negative sign in the end.

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Example Question #11 : Fractional Exponents

Evaluate $\frac{1}{4}^{-\frac{1}{2}}$

Possible Answers:

$-\frac{1}{16}$

$\frac{1}{4}$

$\frac{1}{16}$

Correct answer:

Explanation:

When dealing with fractional exponents, remember this form:

With a negative exponent, we need to remember this form:

$\frac{1}{x^n}$ represents the base of the exponent, and is the power in a positive value.

$\frac{1}{4}^{-\frac{1}{2}}=\frac{1}{\frac{1}{4}^{\frac{1}{2}}}=\frac{1}{\sqrt[2]{\frac{1}{4^1}}}=\frac{1}{\frac{1}{2}}=2$

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Example Question #18 : Fractional Exponents

Evaluate $5^{-\frac{1}{3}}$

Possible Answers:

$-\frac{1}{125}$

$-\frac{1}{\sqrt[3]{5}}$

$\sqrt[3]{5}$

$-\sqrt[3]{5}$

$\frac{1}{\sqrt[3]{5}}$

Correct answer:

$\frac{1}{\sqrt[3]{5}}$

Explanation:

When dealing with fractional exponents, remember this form:

With a negative exponent, we need to remember this form:

$\frac{1}{x^n}$ represents the base of the exponent, and is the power in a positive value.

$5^{-\frac{1}{3}}=\frac{1}{5^{\frac{1}{3}}}=\frac{1}{\sqrt[3]{5}}$

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Algebra II : Fractional Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Rational Exponents

Example Question #11 : Fractional Exponents

Example Question #12 : Fractional Exponents

Example Question #13 : Fractional Exponents

Example Question #14 : Fractional Exponents

Example Question #15 : Fractional Exponents

Example Question #16 : Fractional Exponents

Example Question #17 : Fractional Exponents

Example Question #11 : Fractional Exponents

Example Question #18 : Fractional Exponents

All Algebra II Resources

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