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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #373 : Exponents

What is the product of 3x^2 and 6x^4?

Possible Answers:

18x

18x^4

18x^6

18x^7

Correct answer:

18x^6

Explanation:

Remember, product means multiplication: (3x^2)(6x^4)=18x^6 . Multiply like terms and recall that when bases are the same, add exponents.

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Example Question #49 : Simplifying Exponents

What is the quotient of 24y^9 and $6y^{-4}$ ?

Possible Answers:

$4y^{-13}$

$4y^{3}$

$4y^{11}$

$4y^{13}$

$y^{13}$

Correct answer:

$4y^{13}$

Explanation:

Recall that quotient means division: $\frac{24y^9}{6y^{-4}}$ . To make the negative exponent positive, put it in the numerator: $\frac{24y^9y^4}{6}$ . Now, simplify. Remember that when multiplying and bases are the same, add exponents. Your answer is: $4y^{13}$ .

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Example Question #381 : Exponents

Simplify.

$x^{15}*x^{17}$

Possible Answers:

$x^{32}$

$x^{-2}$

$x^{255}$

$x^{22}$

$x^{285}$

Correct answer:

$x^{32}$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$x^{15}*x^{17}=x^{15+17}=x^{32}$

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Example Question #51 : Simplifying Exponents

Simplify.

$3^{-14}*3^{23}*3^{-15}$

Possible Answers:

$3^{-6}$

$27^{-6}$

3^6

27^6

$9^{-6}$

Correct answer:

$3^{-6}$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$3^{-14}*3^{23}*3^{-15}=3^{-14+23-15}=3^{-6}$

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Example Question #52 : Simplifying Exponents

Simplify.

$\frac{a^{45}}{a^{30}}$

Possible Answers:

$a^{2.5}$

$a^{15}$

$a^{75}$

a^5

$a^{1.5}$

Correct answer:

$a^{15}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{45}}{a^{30}}=a^{45-30}=a^{15}$

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Example Question #53 : Simplifying Exponents

Simplify.

$\frac{a^7}{a^{18}}$

Possible Answers:

$a^{-11}$

$a^{11}$

$a^{-25}$

$a^{25}$

$a^{\frac{7}{18}}$

Correct answer:

$a^{-11}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{7}}{a^{18}}=a^{7-18}=a^{-11}$

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Example Question #54 : Simplifying Exponents

Simplify.

$2^{12}*2^{16}*2^{14}$

Possible Answers:

$8^{44}$

$4^{24}$

$2^{42}$

$2^{36}$

$8^{28}$

Correct answer:

$2^{42}$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$2^{12}*2^{16}*2^{14}=2^{12+16+14}=2^{42}$

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Example Question #55 : Simplifying Exponents

Simplify.

$x^{-24}*x^{21}*y^6$

Possible Answers:

$x^{-3}*y^6$

x^3*y^6

$x^{-504}*y^6$

$x^{-504}$

x^3

Correct answer:

$x^{-3}*y^6$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$x^{-24}*x^{21}*y^6=x^{-24+21}*y^6=x^{-3}*y^6$

We just keep as it is.

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Example Question #56 : Multiplying And Dividing Exponents

Simplify.

$\frac{a^9b^{11}}{a^{10}b^7}$

Possible Answers:

$\frac{b^4}{a}$

$a^{19}b^{18}$

$a^{90}b^{77}$

ab^3

$\frac{a}{b^4}$

Correct answer:

$\frac{b^4}{a}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{9}b^{11}}{a^{10}b^7}=a^{9-10}*b^{11-7}=a^{-1}*b^4$ $a^{-1}$ is the same as $\frac{1}{a}$ .

Final answer is $\frac{b^4}{a}$ .

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Example Question #57 : Multiplying And Dividing Exponents

Simplify.

$\frac{a^{23}b^{12}}{a^{25}b^{15}}$

Possible Answers:

$a^{48}b^{27}$

$\frac{1}{a^2b^3}$

-(ab)^6

ab^6

a^2b^3

Correct answer:

$\frac{1}{a^2b^3}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{23}b^{12}}{a^{25}b^{15}}=a^{23-25}*b^{12-15}=a^{-2}*b^{-3}$ $a^{-2}$ is the same as $\frac{1}{a^2}$ and $b^{-3}$ is the same as $\frac{1}{b^3}$ .

Final answer is $\frac{1}{a^2b^3}$ .

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #373 : Exponents

Example Question #49 : Simplifying Exponents

Example Question #381 : Exponents

Example Question #51 : Simplifying Exponents

Example Question #52 : Simplifying Exponents

Example Question #53 : Simplifying Exponents

Example Question #54 : Simplifying Exponents

Example Question #55 : Simplifying Exponents

Example Question #56 : Multiplying And Dividing Exponents

Example Question #57 : Multiplying And Dividing Exponents

All Algebra II Resources

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