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Algebra II : Mathematical Relationships and Basic Graphs

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Example Questions

Example Question #163 : Multiplying And Dividing Exponents

Simplify $\frac{x^{-3}x^{4}x^{-5}}{x^{-5}}$

Possible Answers:

$x^{-16}$

$x^{-1}$

$x^{16}$

Correct answer:

Explanation:

First combine like variables. There is only one variable in this equation, so you can skip that step. Next, you move negative exponents to the opposite side of the fraction and then add the exponents because we are multiplying. 4+5=9 and 3+5=8 giving us $\frac{x^9}{x^8}$ which simplifies to .

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Example Question #971 : Mathematical Relationships And Basic Graphs

Simplify $x^2y^3x^{-3}y^7$

Possible Answers:

Not possible.

$x^7y^{2}$

$\frac{x^2y^{10}}{x^3}$

x^2y^7

$\frac{y^{10}}{x}$

Correct answer:

$\frac{y^{10}}{x}$

Explanation:

First combine like variables. This leaves us with $x^{-1}y^{10}$ which is equal to $\frac{y^{10}}{x}$

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Example Question #972 : Mathematical Relationships And Basic Graphs

Simplify x^2y^4z^5x^5z^7y^8

Possible Answers:

$1/x^7y^{12}z^{12}$

Not possible.

$(xyz)^{31}$

$x^7y^{12}z^{12}$

Correct answer:

$x^7y^{12}z^{12}$

Explanation:

First combine like variables by adding exponents. This leaves us with $x^7y^{12}z^{12}$

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Example Question #973 : Mathematical Relationships And Basic Graphs

Simplify $\frac{x^7y^2z^8x^2y^{16}}{x^9y^{18}}$

Possible Answers:

z^8

$x^{18}y^{36}z^8$

Not possible

xyz^8

Correct answer:

z^8

Explanation:

First, combine exponents of like variables. This gives us $\frac{x^9y^{18}z^8}{x^9y^{18}}$ which simplifies to z^8

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Example Question #974 : Mathematical Relationships And Basic Graphs

Simplify $x^5y^2x^{-4}$

Possible Answers:

xy^2

x^2y

(xy)^2

$\frac{x}{y^2}$

Correct answer:

xy^2

Explanation:

First, combine exponents of like variables. This gives us xy^2

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Example Question #975 : Mathematical Relationships And Basic Graphs

Simplify $z^3y^2x^6y^{-3}$

Possible Answers:

z^3y^2x^6

$\frac{z^3x^6}{y}$

$\frac{z^3x^6}{y^3}$

(xyz)^8

Correct answer:

$\frac{z^3x^6}{y}$

Explanation:

First, combine exponents of like variables. This gives us $z^3y^{-1}x^6$ which simplifies to $\frac{z^3x^6}{y}$

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Example Question #976 : Mathematical Relationships And Basic Graphs

Simplify $x^8z^2y^3x^4y^{18}z^2z^{-14}y^{-23}y^{12}x^{-3}z^{22}x^{-9}$

Possible Answers:

y^3

$x^{24}y^{45}z^{25}$

x^2

$y^{10}z^{12}$

Correct answer:

$y^{10}z^{12}$

Explanation:

First, combine exponents of like variables and add them together. This gives us $x^0y^{10}z^{12}$ which simplifies to $y^{10}z^{12}$

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Example Question #3639 : Algebra Ii

The expression $\frac{a^{3}b^{-2}}{a^{-4}b^{2}}$ is equivalent to?

Possible Answers:

$\frac{a^{7}}{b^{4}}$

$\frac{b^{5}}{a^{7}}$

$\frac{a^{3}}{b^{2}}$

$a^{-2}b^{-2}$

Correct answer:

$\frac{a^{7}}{b^{4}}$

Explanation:

By simplifying the exponents: bringing the $a^{-4}$ to the numerator and adding the two a's together, getting $a^{7}$ in the numerator, and bringing the $b^{-2}$ to the denominator and adding the two b's together, getting $b^{4}$ in the denominator.

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Example Question #3641 : Algebra Ii

Divide the exponents: $\frac{2^{8}}{2^{10}}$

Possible Answers:

$\frac{1}{512}$

$\frac{1}{4}$

$-\frac{1}{4}$

$\frac{1}{2}$

$\frac{1}{256}$

Correct answer:

$\frac{1}{4}$

Explanation:

Since both of the terms are divided and share a common base, we can simplify the exponents by subtraction.

$\frac{2^{8}}{2^{10}} = 2^{8-10} = 2^{-2}$

The negative exponent can be rewritten as fraction.

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

The answer is: $\frac{1}{4}$

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Example Question #3642 : Algebra Ii

Simplify: $\frac{x^{-5}}{x^{-6}} \div x^{-5}$

Possible Answers:

$\frac{1}{x^6}$

x^6

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

$\frac{1}{x^4}$

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

Correct answer:

x^6

Explanation:

Evaluate the first term by subtracting the exponents.

$\frac{x^{-5}}{x^{-6}} = x^{-5-(-6)} = x^{-5+6} = x^1=x$

$x\div x^{-5} = \frac{x^1}{x^{-5}} = x^{1-(-5)} = x^6$

The answer is: x^6

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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 #163 : Multiplying And Dividing Exponents

Example Question #971 : Mathematical Relationships And Basic Graphs

Example Question #972 : Mathematical Relationships And Basic Graphs

Example Question #973 : Mathematical Relationships And Basic Graphs

Example Question #974 : Mathematical Relationships And Basic Graphs

Example Question #975 : Mathematical Relationships And Basic Graphs

Example Question #976 : Mathematical Relationships And Basic Graphs

Example Question #3639 : Algebra Ii

Example Question #3641 : Algebra Ii

Example Question #3642 : Algebra Ii

All Algebra II Resources

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