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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #261 : Exponents

Expand 12^8

Possible Answers:

12*12*12*12*12*12*12*12

12^8*12^8*12^8*12^8*12^8*12^8*12^8*12^8

12*12*8*8*8*12

8*8*8*8*8*8*8*8*8*8*8*8

12*8

Correct answer:

12*12*12*12*12*12*12*12

Explanation:

To expand the exponent, we multiply the base by the power it is being raised to.

12^8=12*12*12*12*12*12*12*12

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Example Question #262 : Exponents

Expand (-6)^6

Possible Answers:

-6*-6*-6*-6*-6*-6

-6*6

6*6*6*6*6*6

-6*-6*-6*-6*-6*-6*6*6*6*6*6*6

-6^6*-6^6*-6^6*-6^6*-6^6*-6^6

Correct answer:

-6*-6*-6*-6*-6*-6

Explanation:

To expand the exponent, we multiply the base by the power it is being raised to.

(-6)^6=-6*-6*-6*-6*-6*-6

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Example Question #63 : Simple Exponents

Evaluate: $(x^{3})^3+3x^3+3x(3x^3)$

Possible Answers:

x^9+6x^4+3x^3

x^6+9x^4+3x^3

x^6+6x^4+3x^3

x^9+9x^4+3x^3

10x^3+9x^4

Correct answer:

x^9+9x^4+3x^3

Explanation:

Evaluate each term of $(x^{3})^3+3x^3+3x(3x^3)$ .

$(x^{3})^3 = (x^{3})(x^{3})(x^{3}) = x^{3+3+3} = x^9$

The term 3x^3 is already simplified.

3x(3x^3) = 9x^4

Combine all the terms. There are no like-terms.

The answer is: x^9+9x^4+3x^3

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Example Question #263 : Exponents

Convert $4^{10}$ to base .

Possible Answers:

$2^{12}$

$2^{24}$

$2^{10}$

2^8

$2^{20}$

Correct answer:

$2^{20}$

Explanation:

We know that 4=2^2 .

Therefore

$4^{10}=(2^2)^{10}=2^{20}$ .

Remember to apply the power rule of exponents.

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Example Question #66 : Simple Exponents

Convert $2^{18}$ to base $\frac{1}{2}$ .

Possible Answers:

$(\frac{1}{2})^{24}$

$(\frac{1}{2})^{18}$

$(\frac{1}{2})^{-18}$

$(\frac{1}{2})^{-36}$

$(\frac{1}{2})^{-16}$

Correct answer:

$(\frac{1}{2})^{-18}$

Explanation:

We know that $2=\frac{1}{2}^{-1}$ .

Remember when having negative exponents

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

which is the positive exponent raising base .

Therefore

$2^{18}=(\frac{1}{2}^{-1})^{18}=(\frac{1}{2})^{-18}$ .

Remember to apply the power rule of exponents.

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Example Question #67 : Simple Exponents

Evaluate 5^6

Possible Answers:

125625

15625

78125

252525

3025

Correct answer:

15625

Explanation:

To evaluate the exponent, we expand 5^6 into 5*5*5*5*5*5 .

We just multiply the numbers out to get,

$\\ 5\times 5=25 \\25\times 5=125 \\125\times 5=625 \\625\times 5=3125 \\3125\times 5=15625$

Therefore, 5^6=15625 .

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Example Question #68 : Simple Exponents

Evaluate -9^4

Possible Answers:

6561

729

Correct answer:

Explanation:

To evaluate the exponent, we expand -9^4 into -(9*9*9*9) .

We just multiply the numbers out to get,

$\\9\times9=81 \\81\times 9=729 \\729\times9=6561$

Remember to apply the negative sign after solving the exponent.

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Example Question #734 : Mathematical Relationships And Basic Graphs

Evaluate (-8)^6

Possible Answers:

144262

164826

262144

Correct answer:

262144

Explanation:

To evaluate the exponent, we expand (-8)^6 into -8*-8*-8*-8*-8*-8 .

We just multiply the numbers out to get

$\\-8\times -8=64 \\64\times -8=-512 \\-512\times -8=4096 \\4096\times -8=-32768 \\-32768\times -8=262144$ .

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Example Question #735 : Mathematical Relationships And Basic Graphs

Simplify: -3^3+2^3-1^3

Possible Answers:

Correct answer:

Explanation:

Simplify each term.

$-3^3+2^3-1^3= -(3\cdot 3\cdot 3) +(2\cdot 2\cdot 2)-(1\cdot 1\cdot 1)$

The expression simplifies to:

-27+8-1 = -20

The answer is:

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Example Question #266 : Exponents

Simplify the exponents: $(\frac{1}{3})^2+(\frac{2}{5})^2$

Possible Answers:

$\frac{17}{75}$

$\frac{61}{225}$

$\frac{37}{25}$

$\frac{4}{15}$

$\frac{31}{125}$

Correct answer:

$\frac{61}{225}$

Explanation:

Simplify the terms with the exponents.

$(\frac{1}{3})^2+(\frac{2}{5})^2 = \frac{1}{9}+\frac{4}{25}$

To add the fractions, we will need a common denominator.

Multiply the two denominators together.

$25\times 9 = 225$

Convert both fractions to this denominator.

$\frac{1(25)}{9(25)}+\frac{4(9)}{25(9)} =\frac{25}{225}+\frac{36}{225}$

The numerators can be added now that the denominators are the same.

The answer is: $\frac{61}{225}$

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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 #261 : Exponents

Example Question #262 : Exponents

Example Question #63 : Simple Exponents

Example Question #263 : Exponents

Example Question #66 : Simple Exponents

Example Question #67 : Simple Exponents

Example Question #68 : Simple Exponents

Example Question #734 : Mathematical Relationships And Basic Graphs

Example Question #735 : Mathematical Relationships And Basic Graphs

Example Question #266 : Exponents

All Algebra II Resources

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