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Algebra II : Simplifying Exponents

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Example Questions

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:

19^2

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

19^6

$19^{18}$

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

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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Example Question #233 : Simplifying Exponents

Simplify $(x^{-6}x^{4})^{3}$ .

Possible Answers:

$\frac{1}{x^{6}}$

$x^{6}$

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

$\frac{1}{x^{30}}$

Correct answer:

$\frac{1}{x^{6}}$

Explanation:

The problem uses both the Power of a Product Property and the Power of a Power Property of exponents.

$x^{a}x^{b}=x^{a+b}$

$(x^{a})^{b}=x^{ab}$

First multiply the terms inside the parentheses:

$(x^{-6}x^{4})^{3}=(x^{-6+4})^{3}=(x^{-2})^{3}$

Now raise the term to the 3rd power:

$(x^{-2})^{3}=x^{-2\cdot 3}=x^{-6}$

Negative exponents mean that the term belongs in the denominator:

$x^{-6}=\frac{1}{x^{6}}$

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Algebra II : Simplifying Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

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)

Example Question #233 : Simplifying Exponents

All Algebra II Resources

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