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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 #11 : Exponents

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

Possible Answers:

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

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

2a^5b^4

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

None of the other answers.

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 #12 : Exponents

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

Possible Answers:

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

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

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

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

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

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 #13 : 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 #11 : 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 : 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 : Exponents

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

Possible Answers:

$\frac{1}{2}$

$\frac{1}{4}$

$-\frac{1}{2}$

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 #11 : 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 #481 : Mathematical Relationships And Basic Graphs

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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Example Question #482 : Mathematical Relationships And Basic Graphs

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.

$\frac{1}{(-8)^{2}}=\frac{1}{64}$ It is important to keep the paranthesis as we are squaring which makes our answer.

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Example Question #20 : Exponents

Evaluate $(-9)^{-3}$

Possible Answers:

$\frac{1}{729}$

$-\frac{1}{729}$

729

Correct answer:

$-\frac{1}{729}$

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.

$\frac{1}{(-9)^{3}}=-\frac{1}{729}$ Our answer is negative because we have an odd exponent.

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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 #11 : Exponents

Example Question #12 : Exponents

Example Question #13 : Exponents

Example Question #11 : Negative Exponents

Example Question #15 : Exponents

Example Question #16 : Exponents

Example Question #11 : Exponents

Example Question #481 : Mathematical Relationships And Basic Graphs

Example Question #482 : Mathematical Relationships And Basic Graphs

Example Question #20 : Exponents

All Algebra II Resources

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