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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 #164 : Multiplying And Dividing Exponents

Simplify $\frac{x^{-15}}{x^{-22}}$

Possible Answers:

$x^{-7}$

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

x^2

x^7

Correct answer:

x^7

Explanation:

First combine like variables. There is only one variable in this equation, so you can skip that step. Next, move negative exponents to the other side of the fraction to get $\frac{x^{22}}{x^{15}}$ . Finally simplifying gives x^7

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Example Question #165 : Multiplying And Dividing Exponents

Simplify $x^{-16}x^4x^{12}$

Possible Answers:

1/x

x^2

Correct answer:

Explanation:

First combine like variables. There is only one variable in this equation, so you can skip that step. Next, you add the exponents because we are multiplying. -16+4+12=0. x^0=1

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Example Question #501 : 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 #171 : Simplifying Exponents

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

Possible Answers:

$(xyz)^{31}$

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

Not possible.

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

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 #171 : Simplifying Exponents

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

Possible Answers:

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

xyz^8

z^8

Not possible

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:

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

x^2y

(xy)^2

xy^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:

(xyz)^8

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

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

z^3y^2x^6

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:

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

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

x^2

y^3

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 #177 : Simplifying Exponents

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

Possible Answers:

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

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

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

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

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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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #164 : Multiplying And Dividing Exponents

Example Question #165 : Multiplying And Dividing Exponents

Example Question #501 : Exponents

Example Question #971 : Mathematical Relationships And Basic Graphs

Example Question #171 : Simplifying Exponents

Example Question #171 : Simplifying Exponents

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 #177 : Simplifying Exponents

All Algebra II Resources

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