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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #246 : Exponents

Expand $\frac{1}{2}^8$

Possible Answers:

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

$\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$

$\frac{1}{2}^8*8$

$\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8$

$\frac{1}{2}*\frac{1}{2}*8*8$

Correct answer:

$\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$

Explanation:

When expanding exponents, we repeat the base by the exponential value.

$\frac{1}{2}^8=\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$

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Example Question #241 : Exponents

Expand (-4)^3

Possible Answers:

(-4)^3*(-4)^3*(-4)^3

-4*-4*-4

-4*3

4*4*4

3*3*3*3

Correct answer:

-4*-4*-4

Explanation:

When expanding exponents, we repeat the base by the exponential value.

(-4)^3=-4*-4*-4

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Example Question #721 : Mathematical Relationships And Basic Graphs

Change 4^6 to base

Possible Answers:

$2^{20}$

$2^{10}$

$2^{12}$

$2^{14}$

2^8

Correct answer:

$2^{12}$

Explanation:

To convert the base, we know that 4=2^2 . Therefore $(2^2)^6=2^{12}$ . Remember to apply the power rule of exponents.

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Example Question #722 : Mathematical Relationships And Basic Graphs

Change 8^6 to base

Possible Answers:

$2^{18}$

$2^{16}$

2^9

$2^{12}$

$2^{24}$

Correct answer:

$2^{18}$

Explanation:

To convert the base, we know that 8=2^3 . Therefore $(2^3)^6=2^{18}$ . Remember to apply the power rule of exponents.

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Example Question #253 : Exponents

Change $2^{32}$ to base .

Possible Answers:

$4^{16}$

4^8

$4^{32}$

$4^{64}$

$4^{36}$

Correct answer:

$4^{16}$

Explanation:

To convert the base, we know that 4=2^2 . Therefore $(2^2)^x=2^{32}$ . Remember to apply the power rule of exponents. 2x=32 x=16 Answer is $4^{16}$ .

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Example Question #56 : Simple Exponents

Change 27^6 to base

Possible Answers:

$9^{10}$

$9^{12}$

9^6

$9^{18}$

9^9

Correct answer:

9^9

Explanation:

To convert the base, we know that 27=3^3 . Therefore $(3^3)^6=3^{18}$ . Remember to apply the power rule of exponents. Next, we know that 9=3^2 . Therefore, $(3^2)^x=3^{18}$ . Then 2x=18 . x=9 . Answer is 9^9

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Example Question #57 : Simple Exponents

Evaluate 7^3

Possible Answers:

147

343

Correct answer:

343

Explanation:

We can expand 7^3 as 7*7*7 .

First multiply the first two integers:

7*7=49

From here multiply 49 with the remaining 7:

$49 \\ \underline{ \times \ \ \ 7}$

Multiply 7 by 9, leave the 3 in the ones place and carry the 6.

$49 \\ \underline{ \times \ \ \ 7}$

Now multiply 7 by 4 and add the remaining 6.

7*4+6=28+6=34

$49 \\ \underline{ \times \ \ \ 7}$

343

The product is 343 .

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Example Question #253 : Exponents

Evaluate 9^4

Possible Answers:

9891

10321

729

6561

Correct answer:

6561

Explanation:

We can expand 9^4 to 9*9*9*9 .

First multiply the first two integers together.

$9 \\ \underline{\times \ \ 9}$

Now multiply 81 by 9. First multiply the 9 by the one then the 9 by the 8:

$81 \\ \underline{\times \ \ \ 9}$

729

From here multiply 729 by 9.

Ones place: $9\times9=8{\color{Red} 1}$ Keep the one and carry the eight.

Tens place: $9\times 2+8=18+8=2{\color{Red} 6}$ Keep the six and carry the two.

The hundredths place: $9\times 7+2=63+2={\color{Red} 65}$

Combining the values to solve for the product results in:

6561 .

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Example Question #59 : Simple Exponents

Evaluate (-6)^4

Possible Answers:

216

1024

1296

Correct answer:

1296

Explanation:

We can expand (-6)^4 to be (-6*-6*-6*-6) . Remember when an even number of negative values are multiplied together the product becomes positive.

First multiply the first two integers:

$-6\times -6=36$

Now multiply 36 by -6:

$36 \\ \underline{\times -6}$

First multiply 6 by 6, then 3 by 6 plus the remainder.

Ones place: $6\times -6=-3{\color{Red} 6}$

Tens place: $-6\times 3 +3=18+3=-{\color{Red} 21}$

Thus,

$36 \\ \underline{\times-6}$

Now multiply -216 by -6.

Ones place: $-6\times -6 =3{\color{Red} 6}$

Tens place: $6\times 1 +3=6+3={\color{Red} 9}$

Hundreds place: $6\times 2={\color{Red} 12}$

Combining these results in 1296

The product is then 1296 .

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Example Question #254 : Exponents

Evaluate -6^4

Possible Answers:

1296

216

Correct answer:

Explanation:

We can expand -6^4 to be -(6*6*6*6) . Remember the negative is outside the exponent.

First multiply the first two integers:

$6\times 6=36$

Now multiply 36 by 6:

$36 \\ \underline{\times\ \ \ 6}$

First multiply 6 by 6, then 3 by 6 plus the remainder.

Ones place: $6\times 6=3{\color{Red} 6}$

Tens place: $6\times 3 +3=18+3={\color{Red} 21}$

Thus,

$36 \\ \underline{\times\ \ \ \ 6}$

216

Now multiply 216 by 6.

Ones place: $6\times 6 =3{\color{Red} 6}$

Tens place: $6\times 1 +3=6+3={\color{Red} 9}$

Hundreds place: $6\times 2={\color{Red} 12}$

Combining these results in 1296

Substituting this back into the -6^4 to be -(6*6*6*6) the product is then .

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #246 : Exponents

Example Question #241 : Exponents

Example Question #721 : Mathematical Relationships And Basic Graphs

Example Question #722 : Mathematical Relationships And Basic Graphs

Example Question #253 : Exponents

Example Question #56 : Simple Exponents

Example Question #57 : Simple Exponents

Example Question #253 : Exponents

Example Question #59 : Simple Exponents

Example Question #254 : Exponents

All Algebra II Resources

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