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Algebra II : Mathematical Relationships and Basic Graphs

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Example Questions

Example Question #1071 : Mathematical Relationships And Basic Graphs

Evaluate: (4x^3)^3

Possible Answers:

4x^9

64x^9

4x^6

64x^6

12x^6

Correct answer:

64x^9

Explanation:

When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same. However, with a number present, we need to also apply the exponent to the number. We essentially breakdown the components as such: (ab)^x=a^xb^x .

$(4x^3)^3=4^3x^{3*3}=64x^9$

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Example Question #83 : Distributing Exponents (Power Rule)

Evaluate: $(6x^{-3})^{2}$

Possible Answers:

$\frac{36}{x^6}$

$\frac{36}{x^{-6}}$

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

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

$\frac{x^6}{36}$

Correct answer:

$\frac{36}{x^6}$

Explanation:

$(6x^{-3})^{2}=(\frac{6}{x^3})^{2}=\frac{36}{x^6}$

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Example Question #271 : Simplifying Exponents

Evaluate: $(2x^3)^{-4}$

Possible Answers:

$-\frac{1}{16x^{12}}$

$\frac{1}{16x^{12}}$

$\frac{16}{x^{12}}$

$16x^{12}$

$\frac{x^{12}}{16}$

Correct answer:

$\frac{1}{16x^{12}}$

Explanation:

$(2x^3)^{-4}=(\frac{1}{(2x^3)^4})=\frac{1}{16x^{12}}$

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Example Question #272 : Simplifying Exponents

Evaluate: $(-3x^{-4})^{-3}$

Possible Answers:

$-\frac{1}{27x^{12}}$

$-\frac{x^{12}}{27}$

$27x^{12}$

$-\frac{27}{x^{12}}$

$\frac{1}{27x^{12}}$

Correct answer:

$-\frac{x^{12}}{27}$

Explanation:

$(-3x^{-4})^{-3}=-(\frac{3}{x^4})^{-3}=-(\frac{x^4}{3})^3=-\frac{x^{12}}{27}$

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Example Question #86 : Distributing Exponents (Power Rule)

Simplify: $9(3^{3})^{15}$

Possible Answers:

$9^{25}$

$9^{82}$

$3^{47}$

$9^{47}$

$3^{51}$

Correct answer:

$3^{47}$

Explanation:

Simplify the exponent outside the exponent by use of the product rule of exponents.

$9(3^{3})^{15} =9(3^{3\cdot15}) =9(3^{45})$

Change the nine to base three.

$9(3^{45}) = 3^2(3^{45})$

Since powers of a common base are multiplied, the powers can be added.

$3^2(3^{45}) =3^{2+45}= 3^{47}$

The answer is: $3^{47}$

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Example Question #1071 : Mathematical Relationships And Basic Graphs

Simplify: (x^5)^7

Possible Answers:

$x^{12}$

$x^{57}$

x^2

$x^{35}$

$x^{75}$

Correct answer:

$x^{35}$

Explanation:

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

$(x^5)^7=x^{5*7}=x^{35}$

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Example Question #1072 : Mathematical Relationships And Basic Graphs

Simplify: $(x^{-4})^{-3}$

Possible Answers:

$x^{10}$

$x^{-7}$

$x^{12}$

$x^{8}$

$x^{-1}$

Correct answer:

$x^{12}$

Explanation:

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

$(x^{-4})^{-3}=x^{-4*-3}=x^{12}$

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Example Question #1073 : Mathematical Relationships And Basic Graphs

Simplify: (2x^3)^4

Possible Answers:

$16x^{12}$

$2x^{12}$

16x^7

$8x^{12}$

2x^7

Correct answer:

$16x^{12}$

Explanation:

When an exponent is being raised by another exponent, we multiply the exponents and keep the base the same. Since there is a number present, we also must perform the exponent operation as well.

$(2x^3)^4=2^4*x^{3*4}=16x^{12}$

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Example Question #1074 : Mathematical Relationships And Basic Graphs

Simplify: (3x^6)^5

Possible Answers:

$243x^{11}$

$243x^{30}$

243x^8

$15x^{30}$

$3x^{30}$

Correct answer:

$243x^{30}$

Explanation:

When an exponent is being raised by another exponent, we multiply the exponents and keep the base the same. Since there is a number present, we also must perform the exponent operation as well.

$(3x^6)^5=3^5*x^{5*6}=243x^{30}$

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Example Question #1075 : Mathematical Relationships And Basic Graphs

Simplify: 4x^2(3x^6)^2

Possible Answers:

$36x^{24}$

$49x^{24}$

$144x^{10}$

$36x^{14}$

$13x^{14}$

Correct answer:

$36x^{14}$

Explanation:

Since we have two expressions being multiplied, we follow PEMDAS meaning we do exponents first then multiplication. We will apply power rule and then multiplication rule of exponents.

$4x^2(3x^6)^2=4x^2*9x^{12}=36x^{14}$

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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 #1071 : Mathematical Relationships And Basic Graphs

Example Question #83 : Distributing Exponents (Power Rule)

Example Question #271 : Simplifying Exponents

Example Question #272 : Simplifying Exponents

Example Question #86 : Distributing Exponents (Power Rule)

Example Question #1071 : Mathematical Relationships And Basic Graphs

Example Question #1072 : Mathematical Relationships And Basic Graphs

Example Question #1073 : Mathematical Relationships And Basic Graphs

Example Question #1074 : Mathematical Relationships And Basic Graphs

Example Question #1075 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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