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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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All Algebra II Resources

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

Example Questions

Example Question #3691 : Algebra Ii

Simplify: $(3^{-9})^{-9}$ $\displaystyle (3^{-9})^{-9}$

Possible Answers:

$3^{-18}$ $\displaystyle 3^{-18}$

$3^{81}$ $\displaystyle 3^{81}$

$3^{-9}$ $\displaystyle 3^{-9}$

$\displaystyle 3$

$3^{-36}$ $\displaystyle 3^{-36}$

Correct answer:

$3^{81}$ $\displaystyle 3^{81}$

Explanation:

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

$(3^{-9})^{-9}=3^{-9*-9}=3^{81}$ $\displaystyle (3^{-9})^{-9}=3^{-9*-9}=3^{81}$

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Example Question #3692 : Algebra Ii

Simplify: $(\frac{1}{2}^{9})^8$ $\displaystyle (\frac{1}{2}^{9})^8$

Possible Answers:

$2^{17}$ $\displaystyle 2^{17}$

$\frac{1}{2}^{72}$ $\displaystyle \frac{1}{2}^{72}$

4^6 $\displaystyle 4^6$

$2^{72}$ $\displaystyle 2^{72}$

$\frac{1}{2}^{17}$ $\displaystyle \frac{1}{2}^{17}$

Correct answer:

$\frac{1}{2}^{72}$ $\displaystyle \frac{1}{2}^{72}$

Explanation:

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

$(\frac{1}{2}^{9})^8=\frac{1}{2}^{9*8}=\frac{1}{2}^{72}$ $\displaystyle (\frac{1}{2}^{9})^8=\frac{1}{2}^{9*8}=\frac{1}{2}^{72}$

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Example Question #3693 : Algebra Ii

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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Example Question #3694 : Algebra Ii

Simplify:

(4^7)^7 $\displaystyle (4^7)^7$

Possible Answers:

$4^{39}$ $\displaystyle 4^{39}$

$4^{77}$ $\displaystyle 4^{77}$

$4^{28}$ $\displaystyle 4^{28}$

$4^{49}$ $\displaystyle 4^{49}$

$4^{14}$ $\displaystyle 4^{14}$

Correct answer:

$4^{49}$ $\displaystyle 4^{49}$

Explanation:

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

Simplify:

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

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Example Question #3695 : Algebra Ii

Simplify:

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

Possible Answers:

$8^{5}$ $\displaystyle 8^{5}$

$8^{14}$ $\displaystyle 8^{14}$

$8^{-9}$ $\displaystyle 8^{-9}$

$8^{-5}$ $\displaystyle 8^{-5}$

$8^{-14}$ $\displaystyle 8^{-14}$

Correct answer:

$8^{-14}$ $\displaystyle 8^{-14}$

Explanation:

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

Simplify:

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

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Example Question #3696 : Algebra Ii

Simplify:

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

Possible Answers:

$5^{25}$ $\displaystyle 5^{25}$

$5^{10}$ $\displaystyle 5^{10}$

$5^{-12}$ $\displaystyle 5^{-12}$

$5^{18}$ $\displaystyle 5^{18}$

$5^{-10}$ $\displaystyle 5^{-10}$

Correct answer:

$5^{25}$ $\displaystyle 5^{25}$

Explanation:

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

Simplify:

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

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Example Question #3697 : Algebra Ii

Simplify:

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

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

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

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

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

$-\frac{1}{3}$ $\displaystyle -\frac{1}{3}$

Correct answer:

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

Explanation:

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

Simplify:

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

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Example Question #3698 : Algebra Ii

Simplify: (8^8)^8 $\displaystyle (8^8)^8$

Possible Answers:

$8^{64}$ $\displaystyle 8^{64}$

$8^{12}$ $\displaystyle 8^{12}$

$8^{88}$ $\displaystyle 8^{88}$

$8^{24}$ $\displaystyle 8^{24}$

$8^{16}$ $\displaystyle 8^{16}$

Correct answer:

$8^{64}$ $\displaystyle 8^{64}$

Explanation:

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

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

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Example Question #3699 : Algebra Ii

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

Possible Answers:

$9^{81}$ $\displaystyle 9^{81}$

$9^{18}$ $\displaystyle 9^{18}$

$9^{-18}$ $\displaystyle 9^{-18}$

$9^{-19}$ $\displaystyle 9^{-19}$

$9^{-81}$ $\displaystyle 9^{-81}$

Correct answer:

$9^{-81}$ $\displaystyle 9^{-81}$

Explanation:

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

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

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Example Question #3700 : Algebra Ii

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

Possible Answers:

$11^{-22}$ $\displaystyle 11^{-22}$

$11^{121}$ $\displaystyle 11^{121}$

$11^{11}$ $\displaystyle 11^{11}$

$11^{-11}$ $\displaystyle 11^{-11}$

$11^{22}$ $\displaystyle 11^{22}$

Correct answer:

$11^{121}$ $\displaystyle 11^{121}$

Explanation:

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

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

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3691 : Algebra Ii

Example Question #3692 : Algebra Ii

Example Question #3693 : Algebra Ii

Example Question #3694 : Algebra Ii

Example Question #3695 : Algebra Ii

Example Question #3696 : Algebra Ii

Example Question #3697 : Algebra Ii

Example Question #3698 : Algebra Ii

Example Question #3699 : Algebra Ii

Example Question #3700 : Algebra Ii

All Algebra II Resources

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