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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 #31 : Understanding Exponents

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

Possible Answers:

$-\frac{1}{9}$

$\frac{1}{27}$

$-\frac{1}{27}$

Correct answer:

$-\frac{1}{27}$

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.

$-3^{-3}=\frac{1}{(-3)^3}=-\frac{1}{27}$

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Example Question #31 : Negative Exponents

Evaluate $5^{-0.5}$ .

Possible Answers:

$\sqrt{5}}{}$

$-\frac{1}{5}$

$\frac{\sqrt{5}}{5}$

$-\frac{\sqrt{5}}{5}$

$\frac{1}{5}$

Correct answer:

$\frac{\sqrt{5}}{5}$

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.

When an exponent is a decimal, we convert to a fraction.

$0.5=\frac{1}{2}$

This is then written in radical form.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

is the exponent from the numerator of the fraction, is the index from the denominator of the fraction and is the base of the exponent.

$5^{-0.5}=\frac{1}{(5)^{0.5}}=\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}$

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Example Question #31 : Understanding Exponents

Simplify $\frac{1}{4}^{-\frac{1}{2}}$ .

Possible Answers:

$\frac{1}{16}$

$-\frac{1}{2}$

$-\frac{1}{4}$

Correct answer:

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.

When an exponent is a fraction, we convert to radical form.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

is the exponent from the numerator of the fraction, is the index from the denominator of the fraction and is the base of the exponent.

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

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Example Question #31 : Exponents

Simplify:

$10^{-5}$

Possible Answers:

-10^5

$-\frac{1}{10^5}$

$\frac{1}{10^5}$

1000

10000

Correct answer:

$\frac{1}{10^5}$

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

$10^{-5}=\frac{1}{10^5}= \frac{1}{100000}$ .

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Example Question #32 : Negative Exponents

Simplify:

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

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

$-\frac{1}{4}$

Correct answer:

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

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

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Example Question #36 : Understanding Exponents

Simplify:

$(-2)^{-2}$

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

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

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Example Question #501 : Mathematical Relationships And Basic Graphs

Simplify:

$-3^{-3}$

Possible Answers:

$-\frac{1}{9}$

$-\frac{1}{27}$

$\frac{1}{27}$

$\frac{1}{9}$

Correct answer:

$-\frac{1}{27}$

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

$-3^{-3}=-\frac{1}{3^3}=-\frac{1}{27}$

Remember the negative sign is not part of the base value.

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Example Question #38 : Understanding Exponents

Evaluate:

$15^{-4}$

Possible Answers:

-15^4

$-\frac{1}{15^4}$

$15^{4}$

$\frac{1}{15^4}$

Correct answer:

$\frac{1}{15^4}$

Explanation:

In order to convert negative exponents, we will use the following formula:

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

In this formula, is the positive exponent and is the base.

$15^{-4}=\frac{1}{15^4}$

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Example Question #39 : Understanding Exponents

Evaluate:

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

Possible Answers:

216

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

$\frac{1}{6^3}$

Correct answer:

216

Explanation:

In order to convert negative exponents, we will use the following formula:

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

In this formula, is the positive exponent and is the base.

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

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Example Question #40 : Understanding Exponents

Evaluate:

$18^{-1}$

Possible Answers:

$-\frac{1}{18}$

$\frac{1}{18}$

Correct answer:

$\frac{1}{18}$

Explanation:

When exponents are negative, we can express them using the following relationship:

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

In this format, represents the base and represents the exponent. A negative exponent becomes positive when it is rewritten as a reciprocal.

Therefore:

$18^{-1}=\frac{1}{18^1}=\frac{1}{18}$

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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 #31 : Understanding Exponents

Example Question #31 : Negative Exponents

Example Question #31 : Understanding Exponents

Example Question #31 : Exponents

Example Question #32 : Negative Exponents

Example Question #36 : Understanding Exponents

Example Question #501 : Mathematical Relationships And Basic Graphs

Example Question #38 : Understanding Exponents

Example Question #39 : Understanding Exponents

Example Question #40 : Understanding Exponents

All Algebra II Resources

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