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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3371 : Algebra Ii

Convert $\frac{1}{8}$ to base

Possible Answers:

$-2^{3}$

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

$2^{-3}$

$2^{\frac{1}{3}}$

2^2

Correct answer:

$2^{-3}$

Explanation:

We know that exponents raised to the negative power will generate fractions.

We also know that is divisible by .

8=2^3

However, since this a fraction, we then have the following:

$\frac{1}{8}=2^{-3}$ .

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Example Question #3372 : Algebra Ii

Convert 256 to base $\frac{1}{16}$

Possible Answers:

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

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

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

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

$\frac{1}{16}^2$

Correct answer:

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

Explanation:

If fractions are raised to a positive integer exponents, we know we will generate fractions; however, if a fraction is raised by a negative integer exponent, our answer will be whole number instead.

For example:

$\frac{1}{2}^{-2}=\frac{1}{\frac{1}{2^2}}=\frac{1}{\frac{1}{4}}=4$

The following rule has been used in this scenario:

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

In this formula, is a positive exponent raising the base .

We know 256=16^2 .

Since we are dealing with a integer and converting to fractional base, we know we need to have a negative exponent.

The answer is:

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

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Example Question #711 : Mathematical Relationships And Basic Graphs

Expand:

18^8

Possible Answers:

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

18*18*18*18*8*8*8*8

18*8

18*8*8*18

18*18*18*18*18*18*18*18

Correct answer:

18*18*18*18*18*18*18*18

Explanation:

When expanding an exponent, we must multiply the base by itself for the number of indicated by the exponential value.

18^8=18*18*18*18*18*18*18*18

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Example Question #712 : Mathematical Relationships And Basic Graphs

Evaluate:

15^3

Possible Answers:

1025

1515

3375

2525

2575

Correct answer:

3375

Explanation:

When expanding an exponent, we must multiply the base by itself for the number of indicated by the exponential value.

15^3 is expanded out to the following:

15*15*15

The product is 3375 .

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Example Question #241 : Exponents

Convert $8^{12}$ to base .

Possible Answers:

$4^{24}$

$4^{16}$

$4^{18}$

$4^{20}$

$4^{12}$

Correct answer:

$4^{18}$

Explanation:

First, we know that 8=2^3 .

Apply the power rule of exponents:

(a^m)^n=a^m^n

We can then write the following expression:

$(2^3)^{12}=2^{36}$

Second, we know that 4=2^2 .

By applying the same rule, we will get the following expression:

$(2^2)^x=2^{36}$

Therefore:

2x=36 and x=18

The answer is $4^{18}$ .

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Example Question #242 : Understanding Exponents

Change 27^6 to base .

Possible Answers:

$3^{15}$

$3^{27}$

$3^{9}$

$3^{18}$

$3^{12}$

Correct answer:

$3^{18}$

Explanation:

First, we know that 27=3^3 .

Apply the power rule of exponents:

(a^m)^n=a^m^n

We can then write the following expression:

(3^3)^6 or $3^{18}$

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Example Question #3377 : Algebra Ii

Convert $8^{12}$ to base .

Possible Answers:

$2^{24}$

$2^{36}$

$2^{40}$

$2^{18}$

$2^{60}$

Correct answer:

$2^{36}$

Explanation:

First, we know that 8=2^3 .

Apply the power rule of exponents:

(a^m)^n=a^m^n

We can then write the following expression:

$(2^3)^{12}=2^{36}$

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Example Question #243 : Exponents

Convert 16^9 to base .

Possible Answers:

$8^{13}$

$8^{16}$

$8^{12}$

8^9

$8^{24}$

Correct answer:

$8^{12}$

Explanation:

First, we know that 16=2^4 .

Apply the power rule of exponents:

(a^m)^n=a^m^n

We can then write the following expression:

$(2^4)^{9}=2^{36}$

Second, we know that 8=2^3 .

By applying the same rule, we will get the following expression:

$(2^3)^x=2^{36}$

Therefore:

3x=36

Simplify and solve for .

x=12

The answer is $8^{12}$ .

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Example Question #713 : Mathematical Relationships And Basic Graphs

Expand 11^4

Possible Answers:

4*4*4*11*11*11

4*4*4*4*4*4*4*4*4*4*4

11^4*11^4*11^4*11^4

11*4

11*11*11*11

Correct answer:

11*11*11*11

Explanation:

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

11^4=11*11*11*11

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Example Question #714 : Mathematical Relationships And Basic Graphs

Expand 2^7

Possible Answers:

2^7*2^7*2^7*2^7*2^7*2^7*2^7

2*2*2*2*2*2*2

2*2*7*7

2*7

7*7

Correct answer:

2*2*2*2*2*2*2

Explanation:

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

2^7= 2*2*2*2*2*2*2

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3371 : Algebra Ii

Example Question #3372 : Algebra Ii

Example Question #711 : Mathematical Relationships And Basic Graphs

Example Question #712 : Mathematical Relationships And Basic Graphs

Example Question #241 : Exponents

Example Question #242 : Understanding Exponents

Example Question #3377 : Algebra Ii

Example Question #243 : Exponents

Example Question #713 : Mathematical Relationships And Basic Graphs

Example Question #714 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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