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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 #201 : Understanding Exponents

Solve for x:

$3^{3x+1}=81$

Possible Answers:

$x=\frac{1}{3}$

x=3

$x=\frac{80}3{}$

$x=\frac{4}{3}$

x=1

Correct answer:

x=1

Explanation:

Solve for x:

$3^{3x+1}=81$

Step 1: Represent exponentially with a base of

$3\cdot 3\cdot 3\cdot 3=81$ , therefore 3^4=81

Step 2: Set the exponents equal to each other and solve for x

$3^{3x+1}=3^4$

3x+1 = 4

3x = 3

${\color{Red} x=1}$

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Example Question #2 : Simple Exponents

Solve for :

$256=2^{3x+2}$

Possible Answers:

x=6

$x=84\frac{2}{3}$

x=4

x=2

x=12

Correct answer:

x=2

Explanation:

Rewrite 256 in exponential form with a base of :

$2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2=256$

2^8=256

Solve for by equating exponents:

$2^{3x+2}=2^{8}$

3x+2=8

3x=6

${\color{Red} x=2}$

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Example Question #3333 : Algebra Ii

Solve for :

$1024=4^{2x+1}$

Possible Answers:

x=10

x=2

x=7

x=8

x=5

Correct answer:

x=2

Explanation:

Represent 1024 in exponential form using a base of :

$4\cdot 4\cdot 4\cdot 4\cdot 4=1024$

4^5=1024

Solve for by equating exponents:

$4^{2x+1}=4^5$

2x+1=5

2x=4

${\color{Red} x=2}$

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Example Question #2 : How To Find The Number Of Integers Between Two Other Integers

How many perfect squares satisfy the inequality $100 \leq x \leq 1,000$ ?

Possible Answers:

Correct answer:

Explanation:

The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since $10^{2} = 100$ . The largest can be found by noting that $\sqrt{1,000} \approx 31.6$ ; this makes $31^{2} = 961$ the greatest perfect square in this range.

Since the squares of the integers from 10 to 31 all fall in this range, this makes 31 - 10 + 1 = 22 perfect squares.

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Example Question #671 : Mathematical Relationships And Basic Graphs

Simplify (x^2y^3)^3 .

Possible Answers:

x^8y^2^7

x^1^6y^2^4^3

x^6y^9

3x^6y^9

x^5y^6

Correct answer:

x^6y^9

Explanation:

To solve this expression, remove the outer exponent and expand the terms.

$(x^2y^3)^3=x^2\cdot x^2 \cdot x^2 \cdot y^3 \cdot y^3 \cdot y^3$

By exponential rules, add all the powers when multiplying like terms.

The answer is: x^6y^9

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Example Question #7 : Simple Exponents

Solve for :

16=2^22^x

Possible Answers:

Correct answer:

Explanation:

The first step in solving for x is to simplify the right side:

$2^22^x=2^{2+x}$ .

Next, we can re-express the left side as an exponential with 2 as the base.

16=2^4

Now set the new left side equal to the new right side.

$2^4=2^{2+x}$

With the bases now being the same, we can simply set the exponents equal to each other.

4=2+x

x=2

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Example Question #8 : Simple Exponents

Solve for :

$64=\frac{4^6}{4^x}$

Possible Answers:

Correct answer:

Explanation:

To solve for x, we need to simplify both sides in order to make the equation simpler to solve.

can be rewritten as 4^3 , and $\frac{4^6}{4^x}$ can be written as $4^{6-x}$ .

Setting the two sides equal to each other gives us

$4^3=4^{6-x}$

Since the bases are the same we can set the exponents equal to each other.

3=6-x

x=3

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Example Question #672 : Mathematical Relationships And Basic Graphs

Evaluate:

2^5

Possible Answers:

Correct answer:

Explanation:

2^5 is expanded to 2*2*2*2*2 .

We will simply multiply the values in order to get the answer:

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Example Question #3341 : Algebra Ii

Expand:

3^4

Possible Answers:

3*3*3*3

3*4

4*4*4

3^4*3^4*3^4*3^4

3*4*3*4

Correct answer:

3*3*3*3

Explanation:

When we expand exponents, we simply repeat the base by the exponential value.

Therefore:

3^4=3*3*3*3

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Example Question #3342 : Algebra Ii

Expand:

2^8

Possible Answers:

8*8

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

2*8

2^8*2^8*2^8*2^8*2^8*2^8*2^8*2^8*

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

Correct answer:

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

Explanation:

When we expand exponents, we simply repeat the base by the exponential value.

Therefore:

2^8=2*2*2*2*2*2*2*2

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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 #201 : Understanding Exponents

Example Question #2 : Simple Exponents

Example Question #3333 : Algebra Ii

Example Question #2 : How To Find The Number Of Integers Between Two Other Integers

Example Question #671 : Mathematical Relationships And Basic Graphs

Example Question #7 : Simple Exponents

Example Question #8 : Simple Exponents

Example Question #672 : Mathematical Relationships And Basic Graphs

Example Question #3341 : Algebra Ii

Example Question #3342 : Algebra Ii

All Algebra II Resources

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