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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #91 : Exponents

Evaluate: $4^{-4}$

Possible Answers:

$\frac{1}{16}$

$-\frac{1}{16}$

$-\frac{1}{256}$

$\frac{1}{256}$

Correct answer:

$\frac{1}{256}$

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore $4^{-4}=\frac{1}{4^4}=\frac{1}{256}$

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Example Question #92 : Exponents

Simplify: $x^{-3}$

Possible Answers:

x^3

-x^3

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

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

-3x

Correct answer:

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

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $x^{-3}=\frac{1}{x^3}$ .

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Example Question #93 : Exponents

Evaluate: $-x^{-4}$

Possible Answers:

-x^4

$\frac{1}{(-x)^4}$

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

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

x^4

Correct answer:

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

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $-x^4=-\frac{1}{x^4}$ . Remember since there's a negative sign outside the exponent, we apply the negative sign afterwards.

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Example Question #94 : Exponents

Simplify: $(\frac{4}{x})^{-5}$

Possible Answers:

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

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

-4^5x^5

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

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

Correct answer:

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

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $(\frac{4}{x})^{-5}=\frac{1}{\frac{4}{x}^{5}}=\frac{1}{\frac{4^5}{x^5}}=\frac{x^5}{4^5}$

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Example Question #95 : Exponents

Simplify: $(-2x)^{-4}$

Possible Answers:

$\frac{1}{16x^4}$

16x^4

-16x^4

$-\frac{1}{16x^4}$

$\frac{1}{12x^4}$

Correct answer:

$\frac{1}{16x^4}$

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $(-2x)^{-4}=\frac{1}{(-2x)^4}=\frac{1}{16x^4}$ . Remember when applying exponents to the base, we need to apply the exponent to also the coefficient in front of the variable.

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Example Question #96 : Negative Exponents

Simplify: $\frac{7}{49^{-2}}$

Possible Answers:

$\frac{1}{49}$

$\frac{1}{343}$

$\frac{1}{2401}$

16807

2401

Correct answer:

16807

Explanation:

Convert the negative exponent to a fraction.

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

$\frac{7}{49^{-2}} = \frac{7}{\frac{1}{49^{2}}} = 7\times 49^2 = 7\times 2401$

Simplify this term.

The answer is: 16807

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Example Question #97 : Negative Exponents

Evaluate: $(\frac{4}{7})^{-2}+4^{-1}$

Possible Answers:

$\frac{212}{49}$

$\frac{97}{18}$

$\frac{113}{196}$

$\frac{33}{17}$

$\frac{53}{16}$

Correct answer:

$\frac{53}{16}$

Explanation:

Rewrite the expression as fractions. The negative exponent will need to be eliminated in order to be simplified.

$(\frac{4}{7})^{-2} = \frac{1}{(\frac{4}{7})^2} = \frac{1}{\frac{16}{49}} =\frac{49}{16}$

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

Add the expression.

$(\frac{4}{7})^{-2}+4^{-1}= \frac{49}{16}+ \frac{1}{4}$

Convert the second fraction so that both fractions have common denominators.

$\frac{49}{16}+ \frac{4}{16} = \frac{53}{16}$

The answer is: $\frac{53}{16}$

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Example Question #98 : Negative Exponents

Evaluate: $\frac{2(4^{-3})}{8^{-2}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{2}{3}$

Correct answer:

Explanation:

Rewrite the negative exponents as fractions.

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

$8^{-2} = \frac{1}{8^2} = \frac{1}{64}$

Replace the terms.

$\frac{2(4^{-3})}{8^{-2}}=\frac{2 (\frac{1}{64})}{(\frac{1}{64})} =2$

The answer is:

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Example Question #3231 : Algebra Ii

Simplify: $(\frac{2}{3})^{-4}$

Possible Answers:

$\frac{81}{16}$

$\frac{16}{81}$

$\frac{9}{7}$

$\frac{9}{4}$

Correct answer:

$\frac{81}{16}$

Explanation:

We will need to convert the negative exponent into a fraction. This is equivalent to the reciprocal of the positive power.

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

Simplify the complex fraction.

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

The answer is: $\frac{81}{16}$

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Example Question #3232 : Algebra Ii

Evaluate: $5^{-2} \times 2(2^{-1})$

Possible Answers:

$\frac{1}{100}$

$\frac{1}{25}$

$\frac{26}{25}$

$\frac{1}{50}$

$\frac{6}{25}$

Correct answer:

$\frac{1}{25}$

Explanation:

The negative exponents can be rewritten as fractions.

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

Change the expression.

$5^{-2} \times 2(2^{-1}) = \frac{1}{25}\times 2(\frac{1}{2}) = \frac{1}{25}$

The answer is: $\frac{1}{25}$

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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 #91 : Exponents

Example Question #92 : Exponents

Example Question #93 : Exponents

Example Question #94 : Exponents

Example Question #95 : Exponents

Example Question #96 : Negative Exponents

Example Question #97 : Negative Exponents

Example Question #98 : Negative Exponents

Example Question #3231 : Algebra Ii

Example Question #3232 : Algebra Ii

All Algebra II Resources

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