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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #21 : Negative Exponents

Evaluate $(-\frac{1}{2})^{-2}$

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

Explanation:

When dealing with exponents, always turn it into this form:

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

$\frac{1}{(-\frac{1}{2})^{2}}=\frac{1}{\frac{1}{4}}=4$

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Example Question #22 : Negative Exponents

Evaluate $-\frac{1}{6}^{-3}$ .

Possible Answers:

$\frac{1}{216}$

$-\frac{1}{216}$

216

Correct answer:

Explanation:

When dealing with exponents, always turn it into this form:

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

$\frac{1}{(-\frac{1}{6})^{3}}=\frac{1}{-\frac{1}{216}}=-216$

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Example Question #23 : Negative Exponents

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

Possible Answers:

$\frac{9}{4}$

$\frac{4}{9}$

$-\frac{9}{4}$

$-\frac{4}{9}$

$\frac{2}{3}$

Correct answer:

$\frac{9}{4}$

Explanation:

When dealing with exponents, always turn it into this form:

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

$\frac{1}{(\frac{2}{3})^{2}}=\frac{1}{\frac{4}{9}}=\frac{9}{4}$

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Example Question #24 : Negative Exponents

Evaluate $(-\frac{2}{3})^{-2}$

Possible Answers:

$-\frac{4}{9}$

$\frac{2}{3}$

$\frac{4}{9}$

$-\frac{9}{4}$

$\frac{9}{4}$

Correct answer:

$\frac{9}{4}$

Explanation:

When dealing with exponents, always turn it into this form:

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

$\frac{1}{(-\frac{2}{3})^{2}}=\frac{1}{\frac{4}{9}}=\frac{9}{4}$

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Example Question #25 : Negative Exponents

Which of the following is equivalent to the expression $x^{\frac{-3}{4}}$ ?

Possible Answers:

$\frac{1}{\sqrt[4]{x^3}}$

$\frac{1}{x^{\frac{4}{3}}}$

$\frac{1}{\sqrt[3]{x^4}}$

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

Correct answer:

$\frac{1}{\sqrt[4]{x^3}}$

Explanation:

Which of the following is equivalent to the expression $x^{\frac{-3}{4}}$ ?

We need to understand two concepts here.

1) negative exponents: To change the sign of any exponent, simply move it from the numerator to the denominator of a fraction:

$\frac{x^{\frac{-3}{4}}}{1}=\frac{1}{x^{\frac{3}{4}}}$

2) Fractional exponents. The numerator of a fractional exponent will stay as the expoenent. The denominator of a fractional expoenent will become the root that you are taking:

$\frac{1}{x^{\frac{3}{4}}}=\frac{1}{\sqrt[4]{x^3}}$

So our answer is:

$\frac{1}{\sqrt[4]{x^3}}$

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Example Question #26 : Negative Exponents

Simplify $13x^{-2}$

Possible Answers:

$\frac{169}{x^{2}}$

$\frac{13}{x^{2}}$

$\frac{1}{169x^{2}}$

$\frac{x^{2}}{169}$

$\frac{1}{13x^{2}}$

Correct answer:

$\frac{13}{x^{2}}$

Explanation:

A negative exponent simply means to take the reciprocal (flip) the number or variable being taken to the negative power and keep the exponent number while removing the negative. Be careful to only take the reciprocal of what has the exponent

$13x^{-2}$

The exponent in this case is only on the x so only take the reciprocal of the x and leave the 13 in the numerator

$\frac{13}{x^{2}}$

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Example Question #27 : Negative Exponents

$\frac{4x^{-3}}{x^{-8}}$

Possible Answers:

$\frac{64}{x^{11}}$

$\frac{4}{x^{5}}$

$64x^{5}$

$4x^{11}$

$4x^{5}$

Correct answer:

$4x^{5}$

Explanation:

Negative exponents tell you to take the reciprocal of the number or variable. Remember to only take the reciprocal of the number or variable that the exponent is with.

$\frac{4x^{-3}}{x^{-8}}$

You can show each part separately if that helps you.

$4\cdot \frac{1}{x^{3}}\cdot \frac{x^{8}}{1}$

$\frac{4x^{8}}{x^{3}}$

Finally, since the x variable is in both the numerator and denominator, cancel it by subtracting the denominator's exponent from the numerator's exponent.

$4x^{8-3}$

$4x^{5}$

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Example Question #28 : Negative Exponents

Express $x^{-1}$ as a fraction.

Possible Answers:

$\frac{1}{x^{-1}}$

$\frac{1}{x}$

$-\frac{1}{x^{-1}}$

$-\frac{1}{x}$

Correct answer:

$\frac{1}{x}$

Explanation:

When an exponent is negative, we rewrite in this form in terms of a fraction:

$a^{-b}=\frac{1}{a^b}$

is the base while is the exponent and it's going to be a postive number when written in a fraction.

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

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Example Question #29 : Negative Exponents

Express $6^{-3}$ as a fraction.

Possible Answers:

$\frac{1}{216}$

216

$-\frac{3}{216}$

$-\frac{1}{216}$

Correct answer:

$\frac{1}{216}$

Explanation:

When an exponent is negative, we rewrite in this form in terms of a fraction:

$a^{-b}=\frac{1}{a^b}$

is the base while is the exponent and it's going to be a postive number when written in a fraction.

$6^{-3}=\frac{1}{6^3}=\frac{1}{216}$

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Example Question #30 : Negative Exponents

Express $(-2)^{-2}$ as a fraction.

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{4}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{4}$

Explanation:

When an exponent is negative, we rewrite in this form in terms of a fraction:

$a^{-b}=\frac{1}{a^b}$

is the base while is the exponent and it's going to be a postive number when written in a fraction.

$-2^{-2}=\frac{1}{(-2)^2}=\frac{1}{4}$

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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Negative Exponents

Example Question #22 : Negative Exponents

Example Question #23 : Negative Exponents

Example Question #24 : Negative Exponents

Example Question #25 : Negative Exponents

Example Question #26 : Negative Exponents

Example Question #27 : Negative Exponents

Example Question #28 : Negative Exponents

Example Question #29 : Negative Exponents

Example Question #30 : Negative Exponents

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