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Algebra II : Distributing Exponents (Power Rule)

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Example Questions

Example Question #221 : Simplifying Exponents

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

Possible Answers:

$3^{-9}$

$3^{-36}$

$3^{81}$

$3^{-18}$

Correct answer:

$3^{81}$

Explanation:

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

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

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Example Question #222 : Simplifying Exponents

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

Possible Answers:

$2^{72}$

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

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

$2^{17}$

4^6

Correct answer:

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

Explanation:

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

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

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Example Question #223 : Simplifying Exponents

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

Possible Answers:

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

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

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

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

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 #41 : Distributing Exponents (Power Rule)

Simplify:

(4^7)^7

Possible Answers:

$4^{28}$

$4^{14}$

$4^{77}$

$4^{39}$

$4^{49}$

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 #42 : Distributing Exponents (Power Rule)

Simplify:

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

Possible Answers:

$8^{-14}$

$8^{-9}$

$8^{5}$

$8^{-5}$

$8^{14}$

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:

$5^{-10}$

$5^{18}$

$5^{-12}$

$5^{25}$

$5^{10}$

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 #44 : Distributing Exponents (Power Rule)

Simplify:

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

Possible Answers:

$\frac{1}{3}$

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

$-\frac{1}{3}$

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

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

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 #45 : Distributing Exponents (Power Rule)

Simplify: (8^8)^8

Possible Answers:

$8^{24}$

$8^{12}$

$8^{88}$

$8^{64}$

$8^{16}$

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:

$11^{22}$

$11^{-11}$

$11^{-22}$

$11^{11}$

$11^{121}$

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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Algebra II : Distributing Exponents (Power Rule)

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #221 : Simplifying Exponents

Example Question #222 : Simplifying Exponents

Example Question #223 : Simplifying Exponents

Example Question #41 : Distributing Exponents (Power Rule)

Example Question #42 : Distributing Exponents (Power Rule)

Example Question #43 : Distributing Exponents (Power Rule)

Example Question #44 : Distributing Exponents (Power Rule)

Example Question #45 : Distributing Exponents (Power Rule)

Example Question #46 : Distributing Exponents (Power Rule)

Example Question #47 : Distributing Exponents (Power Rule)

All Algebra II Resources

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