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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1 : Negative Exponents

Solve: $32^{-\frac{1}{5}}$

Possible Answers:

$-\frac{32}{5}$

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

To evaluate a negative exponent, convert the exponent to positive by taking the inverse.

$32^{-\frac{1}{5}}= \frac{1}{32^{\frac{1}{5}}}=\frac{1}{2}$

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Example Question #2 : Negative Exponents

Simplify:

$\frac{x^4y^{-3}z^{10}}{x^{-9}y^{11}z^{-3}}$

Possible Answers:

$\frac{x^{13}z^{13}}{y^{14}}$

$\frac{x^{13}z^{13}}{y^{12}}$

$\frac{x^{13}}{y^{14}}$

$\frac{x^{13}z^{13}}{y^{13}}$

Correct answer:

$\frac{x^{13}z^{13}}{y^{14}}$

Explanation:

To simplify this expression, first make all of the negative exponents positive. That means putting them in the opposite position (if they're in the numerator, put it in the denominator and vice versa).

It should then look like:

$\frac{x^4\cdot x^9\cdot z^{10}\cdot z^3}{y^{14}}$ .

Then, combine like terms. Remember, if bases are the same, add exponents!

Therefore, your answer is:

$\frac{x^{13}z^{13}}{y^{14}}$

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Example Question #11 : Negative Exponents

Simplify the expression: $\frac{6a^3b^{-4}}{3a^{-2}b}$

Possible Answers:

2a^5b^4

$\frac{2a}{b^5}$

$\frac{2a^5}{b^5}$

None of the other answers.

$\frac{2a^6}{b^5}$

Correct answer:

$\frac{2a^5}{b^5}$

Explanation:

A negative exponent is resolved by taking the reciprocal. For example $a^-2=\frac{1}{a^2}$ .

$\frac{6a^3b^{-4}}{3a^{-2}b}$

start by making all the negative exponents positive ones:

$\frac{6a^3}{3b*b^4}\div \frac{1}{a^2}$ Note that the whole fraction on the left could have also been written as being divided by a^2 where the one is simply in the denominator, but it is necessary to understand that dividing by a fraction is the same as multiplying by one which occurs in the next step.

$\frac{6a^3*a^5}{3b*b^4}$

Use the multiplication rule of exponents and simplify the constant:

$\frac{2a^5}{b^5}$

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Example Question #11 : Negative Exponents

Simplify: $\frac{12j^{-4}k^2l^{-6}}{90j^8k^{-13}l^2}$

Possible Answers:

$\frac{2k^{15}}{15j^{10}l^8}$

$\frac{2l^8k^{15}}{15j^{12}}$

$\frac{k^{15}}{15j^{12}l^8}$

$\frac{2k^{15}}{15j^{12}l^8}$

$\frac{2k^{15}}{15j^{2}l^8}$

Correct answer:

$\frac{2k^{15}}{15j^{12}l^8}$

Explanation:

First, make all of the negative exponents positive. To do this, put it in the opposite location (if in the numerator, place in the denominator). This should look like: $\frac{12k^{13}k^2}{90j^4j^8l^2l^6}$ . Then, simplify each term. Remember, when multiplying and bases are the same, add exponents. Therefore, your final answer should be: $\frac{2k^{15}}{15j^{12}l^8}$ .

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Example Question #11 : Understanding Exponents

Evaluate $2^{-1}$

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

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.

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

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Example Question #14 : Negative Exponents

Evaluate $3^{-2}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{9}$

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.

$\frac{1}{3^{2}}=\frac{1}{9}$

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Example Question #15 : Negative Exponents

Evaluate $-4^{-3}$

Possible Answers:

$-\frac{1}{64}$

$\frac{1}{64}$

Correct answer:

$-\frac{1}{64}$

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.

$\frac{1}{-4^{3}}=-\frac{1}{64}$ Because the exponent is odd, that's why our fraction is negative.

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Example Question #16 : Negative Exponents

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

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{2}$

$\frac{1}{2}$

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.

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

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Example Question #17 : Negative Exponents

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

Possible Answers:

$-\frac{1}{9}$

$\frac{1}{9}$

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.

$\frac{1}{\frac{1}{3}^{2}}=\frac{1}{\frac{1}{9}}=9$

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Example Question #18 : Negative Exponents

Evaluate $-8^{-2}$

Possible Answers:

$-\frac{1}{64}$

$\frac{1}{64}$

Correct answer:

$-\frac{1}{64}$

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.

$\frac{1}{-8^2}=-\frac{1}{64}$ The reason the answer is negative is because we focus on the exponent first and in this case the exponent is raised to a positive .

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Negative Exponents

Example Question #2 : Negative Exponents

Example Question #11 : Negative Exponents

Example Question #11 : Negative Exponents

Example Question #11 : Understanding Exponents

Example Question #14 : Negative Exponents

Example Question #15 : Negative Exponents

Example Question #16 : Negative Exponents

Example Question #17 : Negative Exponents

Example Question #18 : Negative Exponents

All Algebra II Resources

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