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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Fractional Exponents

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

Possible Answers:

$\frac{1}{27}$

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

$\sqrt{3}$

$\sqrt[3]{3}$

Correct answer:

$\sqrt[3]{3}$

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.

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

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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 #3262 : Algebra Ii

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

Possible Answers:

$\sqrt{2}$

$\sqrt[3]{3}$

$\sqrt[3]{2}$

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 #3262 : Algebra Ii

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

Possible Answers:

$-\frac{1}{16}$

$\frac{1}{16}$

$\frac{1}{4}$

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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Example Question #21 : Fractional Exponents

Evaluate $16^{\frac{3}{4}}$

Possible Answers:

$\frac{\sqrt[4]{16}}{3}$

$\sqrt[4]{16}$

Correct answer:

Explanation:

When dealing with fractional exponents, remember this form:

$16^{\frac{3}{4}}=\sqrt[4]{16^3}$ We can actually get an integer value.

$\sqrt[4]{16^3}=\sqrt[4]{(2^4)^3}=\sqrt[4]{(2^3)^4}$ For the power rule of exponents, they are interchangeable because according to the definition of commutative property, multiplying two different numbers in two different positions will generate the same answer. The fourth powers will cancel leaving us with 2^3 or .

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Example Question #22 : Fractional Exponents

Evaluate $\frac{1}{125}^{-\frac{1}{3}}$

Possible Answers:

$-\frac{1}{5}$

$\frac{1}{5}$

125

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.

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

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Fractional Exponents

Example Question #13 : Fractional Exponents

Example Question #3262 : Algebra Ii

Example Question #15 : Fractional Exponents

Example Question #16 : Fractional Exponents

Example Question #17 : Fractional Exponents

Example Question #3262 : Algebra Ii

Example Question #18 : Fractional Exponents

Example Question #21 : Fractional Exponents

Example Question #22 : Fractional Exponents

All Algebra II Resources

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