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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 #3171 : Algebra Ii

Evaluate:

$24^{-2}$

Possible Answers:

$-\frac{1}{576}$

$\frac{1}{576}$

Correct answer:

$\frac{1}{576}$

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:

$24^{-2}=\frac{1}{24^2}=\frac{1}{576}$

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Example Question #41 : Negative Exponents

Evaluate:

$\left(\frac{1}{7}\right)^{-3}$

Possible Answers:

$-\frac{1}{343}$

343

$\frac{1}{21}$

$\frac{1}{343}$

Correct answer:

343

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:

$\left(\frac{1}{7}\right)^{-3}=\frac{1}{\frac{1}{7^3}}=\frac{1}{\frac{1}{343}}$

Dividing by a fraction is the same as multiplying by its reciprocal.

$\frac{1}{\frac{1}{343}}=1 \times \frac{343}{1}= 343$

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Example Question #43 : Negative Exponents

Evaluate:

$\left(\frac{2}{3}\right)^{-4}$

Possible Answers:

$-\frac{16}{81}$

$-\frac{4}{9}$

$\frac{16}{81}$

$-\frac{81}{16}$

$\frac{81}{16}$

Correct answer:

$\frac{81}{16}$

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:

$\left(\frac{2}{3}\right)^{-4}=\frac{1}{(\frac{2}{3})^3}=\frac{1}{\frac{16}{81}}$

Dividing by a fraction is the same as multiplying by its reciprocal.

$\frac{1}{\frac{16}{81}}=1\times\frac{81}{16}=\frac{81}{16}$

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Example Question #41 : Understanding Exponents

Simplify: $12^{-12}$

Possible Answers:

$-\frac{1}{12^{12}}$

$\frac{1}{12^{12}}$

$\frac{1}{12^{-12}}$

$-12^{12}$

$12^{12}$

Correct answer:

$\frac{1}{12^{12}}$

Explanation:

When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$12^{-12}=\frac{1}{12^{12}}$

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Example Question #45 : Understanding Exponents

Simplify: $\frac{1}{64}^{-3}$

Possible Answers:

262144

$\frac{1}{262144}$

$-\frac{1}{262144}$

Correct answer:

262144

Explanation:

When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$\frac{1}{64}^{-3}=\frac{1}{\frac{1}{64^3}}=\frac{1}{\frac{1}{262144}}=262144$

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Example Question #46 : Understanding Exponents

Evaluate: $\frac{1}{64}^{-\frac{1}{3}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{262144}$

Correct answer:

Explanation:

When dealing with fractional exponents, we rewrite as such: $x^{\frac{a}{b}}=\sqrt[b]{x^a}$ which is the index of the radical and is the exponent raising base . When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$\frac{1}{64}^{-\frac{1}{3}}=\frac{1}{\frac{1}{\sqrt[3]{64}}}=\frac{1}{\frac{1}{4}}=4$

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Example Question #47 : Understanding Exponents

Evaluate: $\frac{1}{8}^{-\frac{2}{3}}$

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{4}$

$-\frac{1}{12}$

Correct answer:

Explanation:

$\frac{1}{8}^{-\frac{2}{3}}=\frac{1}{\frac{1}{\sqrt[3]{8^2}}}=\frac{1}{\frac{1}{4}}=4$

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Example Question #48 : Understanding Exponents

Evaluate: $5^{-8}$

Possible Answers:

$-5^{-8}$

$-\frac{1}{5^8}$

$\frac{1}{5^{-8}}$

$\frac{1}{5^8}$

-5^8

Correct answer:

$\frac{1}{5^8}$

Explanation:

When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$5^{-8}=\frac{1}{5^8}$

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Example Question #49 : Understanding Exponents

Evaluate $21^{-2}$

Possible Answers:

$\frac{1}{441}$

441

$-\frac{1}{441}$

Correct answer:

$\frac{1}{441}$

Explanation:

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

$21^{-2}=\frac{1}{21^2}=\frac{1}{441}$

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Example Question #50 : Understanding Exponents

Evaluate $-4^{-4}$

Possible Answers:

$\frac{1}{16}$

$-\frac{1}{256}$

$\frac{1}{256}$

$-\frac{1}{16}$

Correct answer:

$-\frac{1}{256}$

Explanation:

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

$-4^{-4}=-\frac{1}{4^4}=-\frac{1}{256}$

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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 #3171 : Algebra Ii

Example Question #41 : Negative Exponents

Example Question #43 : Negative Exponents

Example Question #41 : Understanding Exponents

Example Question #45 : Understanding Exponents

Example Question #46 : Understanding Exponents

Example Question #47 : Understanding Exponents

Example Question #48 : Understanding Exponents

Example Question #49 : Understanding Exponents

Example Question #50 : Understanding Exponents

All Algebra II Resources

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