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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 #221 : Simplifying Exponents

Simplify: $(3a^2b^{-3}c^4)^2$

Possible Answers:

$\frac{a^4c^8}{b^6}$

$\frac{9a^4c^8}{b^3}$

$\frac{3a^4c^8}{b^6}$

$\frac{9a^4c^8}{b^6}$

Correct answer:

$\frac{9a^4c^8}{b^6}$

Explanation:

To simplify this expression, square every term in the parentheses:

$3^2a^4b^{-6}c^8$ .

Then simplify and get rid of the negative exponent by putting the b term on the denominator:

$\frac{9a^4c^8}{b^6}$ .

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Example Question #231 : Simplifying Exponents

Simplify:

(4^7)^7

Possible Answers:

$4^{49}$

$4^{14}$

$4^{28}$

$4^{39}$

$4^{77}$

Correct answer:

$4^{49}$

Explanation:

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(4^7)^7=4^{7*7}=4^{49}$

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Example Question #41 : Distributing Exponents (Power Rule)

Simplify:

$(8^7)^{-2}$

Possible Answers:

$8^{-14}$

$8^{-5}$

$8^{-9}$

$8^{14}$

$8^{5}$

Correct answer:

$8^{-14}$

Explanation:

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(8^7)^{-2}=8^{7*-2}=8^{-14}$

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Example Question #43 : Distributing Exponents (Power Rule)

Simplify:

$(5^{-5})^{-5}$

Possible Answers:

$5^{18}$

$5^{-10}$

$5^{-12}$

$5^{10}$

$5^{25}$

Correct answer:

$5^{25}$

Explanation:

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(5^{-5})^{-5}=5^{-5*-5}=5^{25}$

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Example Question #1031 : Mathematical Relationships And Basic Graphs

Simplify:

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

Possible Answers:

$\frac{1}{3}^{49}$

$-\frac{1}{3}$

$\frac{1}{3}$

$\frac{1}{3}^{-14}$

$\frac{1}{3}^{-49}$

Correct answer:

$\frac{1}{3}^{-49}$

Explanation:

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$\left(\frac{1}{3}^7\right)^{-7}=\frac{1}{3}^{7*-7}=\frac{1}{3}^{-49}$

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Example Question #41 : Distributing Exponents (Power Rule)

Simplify: (8^8)^8

Possible Answers:

$8^{12}$

$8^{88}$

$8^{24}$

$8^{16}$

$8^{64}$

Correct answer:

$8^{64}$

Explanation:

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(8^8)^8=8^{8*8}=8^{64}$

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Example Question #46 : Distributing Exponents (Power Rule)

Simplify: $(9^9)^{-9}$

Possible Answers:

$9^{-19}$

$9^{-81}$

$9^{18}$

$9^{81}$

$9^{-18}$

Correct answer:

$9^{-81}$

Explanation:

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(9^9)^{-9}=9^{-9*9}=9^{-81}$

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Example Question #47 : Distributing Exponents (Power Rule)

Simplify: $(11^{-11})^{-11}$

Possible Answers:

$11^{121}$

$11^{11}$

$11^{22}$

$11^{-11}$

$11^{-22}$

Correct answer:

$11^{121}$

Explanation:

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(11^{-11})^{-11}=11^{-11*-11}=11^{121}$

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Example Question #231 : Simplifying Exponents

Simplify: $144^6\div12^7$

Possible Answers:

$12^{-3}$

12^6

$12^{-1}$

$12^{-2}$

12^5

Correct answer:

12^5

Explanation:

Although we don't have the same base, we know that 144=12^2 . Therefore we have $144^6\div12^7=(12^2)^6\div12^7=12^{12}\div12^7$

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$12^{12}\div12^7=12^{12-7}=12^5$

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Example Question #51 : Distributing Exponents (Power Rule)

Simplify: $(19^\frac{2}{3})^9$

Possible Answers:

19^6

$19^{\frac{1}{2}}$

19^2

$19^{18}$

$19^{\frac{4}{7}}$

Correct answer:

19^6

Explanation:

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(19^\frac{2}{3})^9=19^{\frac{2}{3}*9}=19^6$

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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 #221 : Simplifying Exponents

Example Question #231 : Simplifying Exponents

Example Question #41 : Distributing Exponents (Power Rule)

Example Question #43 : Distributing Exponents (Power Rule)

Example Question #1031 : Mathematical Relationships And Basic Graphs

Example Question #41 : Distributing Exponents (Power Rule)

Example Question #46 : Distributing Exponents (Power Rule)

Example Question #47 : Distributing Exponents (Power Rule)

Example Question #231 : Simplifying Exponents

Example Question #51 : Distributing Exponents (Power Rule)

All Algebra II Resources

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